As yuriman said, you can have more vid ram than system ram, and vice versa.
It'll run, but of course, with system RAM that low id assume your not playing games (or very intensive ones), any card that has 2GB's of VRAM will likely be serious overkill in both VRAM and performance required.
Then again, most cards, even entry level, come standard with 2GB's of VRAM anymore, so hmmm, maybe its plenty fine.
Though if your buying higher end vid cards, say... a GTX 770 or 780 (or even 670 or 680), and expect to do some highend gaming (which those cards are capable of)... that 1GB of system RAM wont cut it for any games requiring such graphical power and vram, and VRAM does not add total amount of RAM to your system, as they are used for separate purposes in games.
Basically your video cards would be sitting there, twiddling its thumbs, waiting for the rest of the system to keep up.