The resolution has no importance on GPU memory (at least with todays 1+GB boards).
The resolution itself needs around 100MB (maybe 2x or 3x due to buffering and internal GPU handling). So you would not use more than 0.5GB even at 2xAA.
The problem is the GPU processing power, as 3x 4K monitors increase the frame pixel count by 100% compared to 3x FullHD (I'm currently gaming with 1 7950 and 3x FullHD). Also, the memory bandwidth is not scalable, so doubling the pixel count would result is less than 50% fps.
So I'm sure my 3GB 7950 could handle easily 3 4K monitors, but I would have to drop the detail levels. Please bear in mind that the 4K benchmarks floating around are for high detail.
PS: if you see 1x4K benchmarks with 4xAA or more...