Yes and no. The extra card will give you more FPS in some games, others not so much. There have been alot of reviews where 3 GPU's can actually degrade performance and get you less FPS. Do a search for 6990+6970 vs SLI 580 and you'll see what I'm talkin about.
The 3gb 580's might help you out because of the higher ram amount for that huge resolution.
There are some games/settings where the the extra VRAM would come in handy, but 1.5GB is good for most games up to 5760X1080 4X16X. I've been switching back and forth between a GTX590 and 2GB GTX560Ti SLi for this resolution.
As for the OP, the scaling on a third GTX580 will be much lower than on two, around another 30%. I personally don't think a third 1.5GB GX580 is your best upgrade path given your high resolution. I'd go 3 X 2.5GB GTX570 if you're looking to stay with NVIDIA and surround.