You can use GeForce and Radeon on the same PC only through
HPX.
I'm not sure about multi-monitoring, since haven't tried that so far, but as far as using just one monitor goes, yes you can (that's what I'm doing right now, actually).
Also, it is best for an HPX-setup to have just two cards (one Radeon and one GeForce), because, as of today, it doesn't work correctly with CFX/SLI setups, usually flickering glitches appear.