Take a look at alternate frame rendering.
Basically the cards take it in turns to render frames, or lines on the screen, so each card has less to do, however because each frame is still a full image each card must still be large enough, ram wise, to handle the frame. It is not like gpu1 can 'borrow' gpus2s ram to handle more stuff.
There are variations on it but I think that basically describes it.
Since 1080p takes up 1.5gb in battlefield 3 at 1080p; for your resolution I'd expect you need a 3gb card. You'll probably be over 2gb vram usage.