OK so hereís some more calculations:
The Ikaros sail, currently deployed, has a thickness of 0.0075 mm, or 7.5x10^-6 m.
I couldnít find the density of the sail, so I just went with Beryllium (1.85 kg/m^3). (On the Ikaros web page they say that they used polyimide, which has a density of 1.43 x 10^3 kg/m^3, but I was pretty sure they coated it with some metal)
The area of the Ikaros sail is just under 200 m^2, being 14 m on one side.
If we scale up the sail to a side of 1 km, keeping the same thickness, the area is then 10^6 m^2, so the volume of the sail would be:
10^6 m^2 * 7.5x10^-6 m = 7.5 m^3
And the mass would be:
7.5 m^3 * 1.85x10^3 kg = 1.39 x 10^4 kg
Assuming the payload is 8.61x10^4 kg, for a total mass of 10^5 kg, we have (based on Jim Davisí formula for final velocity):
Vfinal = sqrt(2 * S * k0 * R0 / m *9.9)
= sqrt (2 * 10^6 m^2 * 4.6x10^-6 Pa * 1.5x10^11 m)/10^5 kg * 9.9) = 1.17 x 10^4 m/s, which is nowhere near the speed of light, but it is 2.46 AU/year.