The typical/general constraint is going to be if you have two video ports on your machine. If you do, then yes, that's generally very easily done.
If you don't, you may be able to add/upgrade your video system to something that does. Any PCI-E Video card you buy new today, will support two monitors - the crappiest of those can be picked up for in the $30 range.
A final semi-option is you can get any number of weird adapters that can let you drive multiple monitors in various ways. These, for example, let you split a single video signal on to multiple screens. There are also weird things out there like "USB montitors", that you plugin over USB - I've never tried one as that concept sounds like a horrible idea to me - but I've seen some of that gear around.
So really, yes, you are eligible, unless you don't have two video ports, are unwilling to buy upgrade hardware or have a severely crummy old machine.
As for how well it'll run, I suppose that wasn't really the question - but it'll be a function of the total resolution, color depth and some other similar parameters, but it should generally be fine for non-opengl applications.