Anything is possible, but it is not easy to see why the Delta would use LC-39. The Delta is designed strictly for horizontal processing and LC-37B could be activated (and use the existing horizontal integration building) much more cheaply than building a separate facility at LC-39. There already are horizontal processing facilities, four of them in fact, at LC-39. It would require a different mobile platform than the VAB does, but if you'd read the 21st Century documents, they discussed just this setup.
As Ed Kyle noted earlier, there is no way to erect a horizontal rocket at LC-39. Because of the height of the pad surface above the surrounding terrain and the steep slopes around it there is no way to add rails for a gantry crane and given the location of the flame trench, with one section centered on the crawlerway, no simple way to even add an erector arm.
I've seen some of the documents and even been in some of the meetings referred to. Unfortunately this plan is limited to powerpoint sketches where you can draw anything and is not realistic once you consider it in any depth. The central problem is the concept of a multiuser launch facility. That only works when all users need exactly the same thing, and when the facility itself is the most expensive element.
An example of a facility that could be multiuser but is seriously underutilized is the SLF, which is flat concrete with no interfaces at all. No one is on the runway more than a few hours before being towed off to a specialized hangar. The SLF just needs to be rid of the ancient MSBLS.
But a pad is different. Every launch vehicle has unique structural and functional interfaces and different operational requirements, and they all periodically change. The most radical adaptive capability I ever saw in operation was CX-17B which could accommodate both the Delta II and Delta III, requiring five different fueling systems (RP-1, LH2, Aerozine-50, LOX, and N2O4) and access platforms that could be folded into multiple configurations. The vehicle is the expensive part of the system, and the complex is built around it.
The proposed multiuser launch complex plan for LC-39 is not an engineer's response to the problem of high launch costs, it is the response of management to the problem that the world has changed. Yes, with enough money you could make it work, after a fashion. But why? No launch provider would commit to using a pad when a mod needed by a competitor or the launch failure of a competitor's vehicle might shut them down for six months. There's more than enough conflicts over the common use of the Eastern Range command, control, computers and aircraft, and they can presumably switch vehicles in a day or so. Can you imagine the schedule delays when only one vehicle can be on the pad at once, perhaps for weeks? And for a commercial customer, time is money.
Musk is not a magician. SpaceX is able to work more efficiently than NASA because it is, pardon the pun, "vertically integrated". That is to say that to the greatest extent possible the company has direct control of all the resources needed for the launch and answers only to the customer. Unless he has absolutely no choice Musk will not put himself in a situation he cannot control. And most likely when he has launched a couple of manned Dragons from CX-40 NASA will relent and go along. Similarly, although Boeing is happy to have OPF3 as a single-user processing facility for the CST, in my opinion it will be launched from the existing Atlas pad at CX-41.
The irony is that there are so many things KSC could be doing that could be of enormous practical value to America, from basic R&D in over a dozen fields, no longer tied to the need to claim every test supports the current mission, to clearing away the past and offering each launch provider empty land, utility hookups, and maybe someday a modern range based on GPS tracking and capable of switching vehicles in less than a day. We could be testing the subscale VTOHL reusables the DOD keeps talking about, or even fuel-cell aircraft propulsion, harnessing KSC experience in cryos and runway ops.
KSC can be relevant and indeed vital to our nation in the 21st Century, but only if we have the vision to broaden its mission. KSC can, and must, be much more than just a launch site.