No, short answer and obvious answer is no. 4GB is useless on the 960 because it does not have the raw GPU power to be of any use. At 1440p and 4K the performance of the 4GB 960 over 2GB is literally a max of 5 fps and the 128-bit bus is too tiny to even fully utilize all 4 gigs. You are better off getting the 970 if you can (even if it's 3.5GB before the 4GB problems, it's like 70% faster than a 960).
Nobody should buy a 960 4GB. For any reason. Not hating or anything, but it is utterly useless. It could be useful on 1080p high textures (like skyrim with mods)or something like that, but if you bother buying a more high-res monitor I doubt you would be buying a mid-range GPU for it.
Source: I own a 960 myself as a daily GPU and at 2GB and I am yet to see any real problems with it at 1080p ( I play games on 4x MSAA and 2nd to the highest textures ALL THE TIME no prob). I've seen the benchmarks with the 4GB variant and it's performance just makes it useless for the high-ram. Will probably just be useful for future-proofness but that's the f word in tech and once a game goes past 2GB, using a higher range card is more of a need than a recommendation.
I doubt anybody owns a 4GB 960 anyways. Sorry for the hate. I just like my 960 on its own at 2GB.
Regular 960 is fine (if we ignore AMD prices *cough cough* US prices). Hopefully this prevented you and some others.