The topic pretty much covers the question. I'm running Windows 7 Ultimate, and before I put down money on this game, I have to know if it will run on it.
My original copy cannot, stating 'Screen Init failed' every time I attempt to run it. Has the GOG copy been updated to work with Windows 7?

All games based on the DOS operating in DOSBox. DOSBox works well in Win7.
GOG has a problem with games based on Windows 95/98. Some don't work properly in Windows 7 (for example, Messiah and Interstate '76 Arsenal).
In conclusion M.A.X. 1 works well. M.A.X. 2 don't know, because I did not installed it.

Yup, just tried MAX2 in 7 Ultimate 64 bits, it works flawlessly.