Does a gravity wave/space-time ripple transfer momentum?
Yes, but the issue is not whether it does or does not. The issue is how big it is and whether it would make sense. An electron has mass. The whole Universe has mass. However it does not make sense to say that something that one observes happening in the whole Universe also must similarly happen to an electron. One has to take into account the scale of the phenomenon.
People should compare the extremely small amplitude of the gravitational wave measured from the plunge and coalescence of two big black holes vs. what would be the amplitude of a gravitational field produced by an electromagnetically resonant cavity. It is evident that the gravitational wave from an EM Drive is so extremely small that is nothing compared to the momentum from any other disturbance present in the experimental environment. When people discuss gravitational waves from the EM Drive they just write words: I invite them to make a calculation of its magnitude so that they understand how negligibly small it is. Engineers and scientists use numbers rather than words. At least let's compare orders of magnitudes.
Comparing both would be like comparing the mass of a big black hole to the mass of the EM Drive 
mass of black holes involved in recent gravitational wave measurements: 36 and 29 solar masses
3*1031 kg 

so comparing the mass of the black holes involved in the recent gravitational wave experiments to the mass of the EM Drive is like comparing the mass of the proton to your mass
or like comparing your mass to the mass of the Sun. Both you and the Sun have mass. The Sun attracts all the planets: it is responsible for us being here. Neither you or I appreciable attract any planets, and we should not make arguments that because the Sun makes the planets go into orbits we should similarly make particles go into orbits around us.

Jose':
For locally derived gravitational effects I concur that E&M generated gravitational effects are extremely small in magnitude. However for globally derived inertial reaction forces that come about from the gravitational interactions of all the mass/energy in the causally connected universe, these E&M driven transient inertial forces can be as large as normal Newtonian reaction forces per Woodward's Mach-Effect conjecture.
Best, Paul M.
I'm liking the discussion of Rodal, Star-Drive, and S.Paulissen. This is a very necessary discussion to be having. Rodal, you're right on all counts and the problem isn't lost on me. That's why I was doing crazy sounding things like trying to figure out how the gravitational equivalent of a ferromagnetic core might work several months ago. I know the gravitational effects from an EMdrive are weak. I want it to be strong. I want to be able to describe why it appears to be stronger than it's supposed to be (as predicted by theory), if I'm going to say with zero uncertainty that a gravitational interaction is behind the anomalous thrust. I understand how stiff spacetime is as described by the 8piG/c4 part of the Einstein field equation. I want things to hover, which would mean that an EMdrive would have to induce more gravity than the entire Earth. That's absurd to even think possible (waving hands around and getting vocal like Walter Lewin lol). I get the problem. Even if I had the ability or resources to successfully deploy such a crazy sounding thing and it worked, it still doesn't answer the question of why? Why is more important. The last thing I want to see is something doing an amazing thing and not understanding why. That drives me crazy. I tend to use thinking in extreme cases, be it the very large or the very small, to help figure out problems. Not black and white thinking, I'm talking about the problem solving tool. I like abstraction and intuition to think about things. That's just how I'm wired as an INTJ. It's a strength and a weakness. In this case, I believe it may be helpful to limit the scale to the very, very small. I choose to limit my scale to that of one electron, and focus on the gravitational interaction of one measly electron, combined with the measly, paltry, infinitesimally insultingly small gravitational effects created by an EMdrive, if there even are any. Now I will go bigger again, while keeping in mind the very small. Can an extremely weak changing gravitational disturbance (that is localized to a very small region and also falls off in amplitude as 1/r) be causally connected to, and able to interact with a much stronger gravitational field (say from the electron, or the Earth and the rest of the universe that falls off as 1/r2), I say it can. How could it not? They occupy the same space, and gravity interacts with itself. If I am able to induce an alternating gravitational field, does it necessarily need to have a wide range of influence? No. It (as in some measurable influence on a gravitational wave detector able to see the wave, which doesn't exist yet anyway) doesn't necessarily have to be having an influence near an EMdrive, or be detectable near an EMdrive, it can be happening inside just the same. 1/r falls off more slowly than 1/r2 anyway.
I definitely think there's something we don't understand about how dynamic systems work in GR (I ultimately want this to be understandable in the full theory), and it must be related to changing energy density and changing energy flux over time. I'm intentionally exposing my ignorance here because the answer may be out there but what did Einstein teach us about such things? What did Einstein teach us about the induction of nonconservative gravitational fields? What does Einstein's coupling coefficient tell us about changes in energy density over time? Nothing I can see, and I'll get to this later. What is special or different (if anything) about a changing energy density that's being accelerated or being jerked? We've seen this before in history. I don't believe these things. I know of them. Remember Tajmar's results that were 20 orders of magnitude greater than what was predicted? Or the Podknetnov debacle? Or the Ning Li story? These are all really controversial stories, and for good reason. I treat them as useful fiction. I use useful fiction as part of my thinking too. I think there's value in finding the grain of truth in things that aren't necessarily even real, by aggregating information in an objective way by cutting out the crap and looking at the objective commonalities. It's easy for me to boil down lots of noise into something useful because of how my brain happens to work. What's really behind all of this craziness that's not predicted by accepted theory and is (rightfully) generally dismissed? There's a mystery to be solved here. There's a problem. What limits does Nature place on the curvature of space besides the ones we know? What are the boundary conditions for a dynamic system?
Now I will get to the "get to this later part" and this is going to be ugly. In order to answer your question Dr. Rodal, first I must be able to find the reason why I cannot offer you an answer in the first place. I have to ask myself, and all of you why is it that it is not possible for a copper can to be able to overcome the stiffness of spacetime? What is it about the equations, that prevents an EMdrive from having any noticeable effects on the curvature of spacetime. Put another way, why isn't EMdrive's behavior not predicted by the equations of General Relativity, which I know are true and tested and proven to describe most of our universe (except for the "dark" stuff and things like EMdrive). I must challenge my assumptions. I must ask difficult questions. I must dare to commit heresy. I'm interested in the oldest assumption, which came from a great thinker hundreds of years ago, who lived in a time where the axioms of physics were very different from today. So I present you with the Einstein field equation. You are all familiar with this, many more so than I. We know now that gravity really has nothing to do with mass at all, it's about energy density (and the other components of the stress energy tensor). The more general concept is energy. Energy is more fundamental than mass, as mass is a property of confined energy.

Of interest is the Einstein constant, which is the coupling coefficient in the above field equation:
Within is Newton's gravitational constant G.
Of particular interest to me is the capital M in the denominator. I have a hunch that this can be generalized further to take into account time dependent systems where energy density and energy flux changes over time. I'm uncertain if G is applicable in systems where velocities are high with respect to c too. I think this M is a problem. I don't think this is general enough. I want to explore this and figure out why and what it all means. I think it's important to eradicate the use of the word "mass" wherever possible, with the understanding that the concept of mass is useful, and incorporating the idea of mass into our equations is useful and does make accurate predictions in the Newtonian limit, the idea of mass assumes a time independent invariant, which is true for matter, but it's not true for all systems. So this is where I've gone, and I honestly don't feel very good about what I'm thinking about yet, and it may not survive my own scrutiny or of others, but I will explore this and I invite other brave thinkers to do so. I've identified a problem in my own mind and not yet a solution because I'm unsure as if yet I'm asking the right questions. If I'm off the rails right now, which I may very well be, what happened?
Paul, I think it's a mistake to take it as a given, or an axiom that inertia is Machian in origin. I don't wholly discount the idea however. Can you tell us more about what you presented in that slide or have some links to more about that?