For the most part, yes, you can do that. Assuming you have the PCIe slots and your PSU can power everything, that is.
You might run into some weird issues if you try to run a program on one GPU and move it to the other's monitor, or run something across both monitors, or try to use some kind of super-resolution monitor-spanning setup.
If you also have "onboard" graphics (really CPU graphics now) and a motherboard DVI or VGA port, you might have better luck using that plus the GPU. Generally that's better-supported, though you may need to check your BIOS to see if it requires specific settings.