I can't reproduce it. I tried it on Windows 8.1 with a network drive on W: pointing to a remote machine and signing out and in again. Construct 2 seemed to work just fine. The only reason it should access 'My documents' is to look for a license, and I tried it with a license on the mapped drive as well and it still found it and loaded it OK.
Generally the main problem C2 crashes on 'File - New' or 'File - Open' is due to buggy graphics drivers, since that's the first point it creates an OpenGL context. Are your graphics drivers up to date?