There may be a few very rare cases where you could run into performance issues at high enough settings with 2GB on 5760x1080p. In those cases, simply dropping AA a touch usually fixes it.
As BigMack70 said, "at playable settings", it is very rare. You'll occasionally see a benchmark done with 8xMSAA, Ubersampling, SSAA enabled, and note how 2GB was not enough, but the FPS were only in the 40 or less range. Simply backing off the AA, you get better FPS, to a point of being much more enjoyable regardless if you had the 4GB or not, and not have an issue.
I frankly find these benchmarks very misleading. I think most people would rather have 60+ FPS with 4x MSAA or lower, than 30-40 FPS with 8x MSAA. Visually, there is very little difference, but performance is much more enjoyable at 60+ FPS.