Some super-cheap manufacturers made entire runs of boards with the same host-part in the MAC, assuming nobody'd notice.
ISAslot, conflicts must be handled gracefully by the network protocols and OSs. IP will do so as a protocol, but some OSs are unlikely to like it. In a switched Ethernet environment you'll have a lot of trouble because the switch will learn that the MAC is down one port... no, it's down another... no, back to the first. And at any given time, you don't know which port or both is going to get traffic destined to that MAC. My guess is that in practice, with an Ethernet switch, it just won't work.
Many OSs (either directly or through third-party programs) allow you to manually configure the MAC address. You could certainly do this to try it and see for yourself. You could just as easily do this to fix a MAC conflict if you knew you had one. 10/100 Ethernet cards come free in specially marked boxes of cereal these days, so if you really have a MAC conflict, another solution would just be to replace and destroy one if not both cards (to make sure they doesn't reappear somewhere else in your network, and where there's one duplication there's a good chance there are more from the same manufacturer).