I'm wondering if you can mine on a multi monitor setup if all 4 displays are connected to a single GPU? This would be when the system is otherwise doing nothing and not 24/7 mining.
Yes, you can mine something.
Whether or not you can mine effectively on certain algorithms is another matter, however. The easiest way to check would be to do so experimentally.
As long as it can be done. In my experience with my own rigs I find that low memory and high core algos tend to slow down regular PC use so my best bet is Equihash mining