I know I am late in the party, but The install of C2 (and I think C2 itself) is portable, which means I think it can be transferred in such a way.
Also the free version of C2 combined with a license file (which will be given upon purchase, and can be downloaded afterwards when needed on the scirra store) is what makes the personnal or business version of C2, and I think the license file can be copied over to an usb too (just make sure nobody other than you is using it though). So you should not have problem transporting the paid version with you as long as you have both the free version and the license file.