Never tried it, but doubtful considering the Max 9 initially didn’t work on Vista, until they bought out a service pack so it may run on the then new OS.
A 64 bit system is a must for Max users these days, but what’s the point if using Max 3?
Any Max version before Max 9 is 32 bit anyway, so you won’t get any benefit from it.
Just noticed you wrote “and 2010”. But then why you still need v3?
I think the best thing would be to keep your old Win2000/XP machine for running Max 3 on. And Get your new 64 bit system for Max 2010.
I suppose there is no harm in trying Max 3 on your new system to see if it works, but I wouldn’t count on it.