Lacking details, so nobody can promise anything, but I have run my current desktop with three monitors on two video cards. I currently run it with two monitors and two cards, with one bound to a Windows VM. That is somewhat trickier to set up, but multiple monitors should be fine.

My advice echoes others - you can try before you buy (install) with a few flavors of Linux; see what happens. If you have trouble, try to find a fellow human who can help - X is a little surprising to configure, if you haven't done it before.