I think you mean "4K downsampled to 2560x1440"
And NO, it can't be identical if you are comparing two different monitors with a different amount of pixels.
4K at the same settings gets only HALF the frame rate usually for gaming as 1440p so there are currently very few scenarios that make sense to game at 4K.
It would generally make more sense to run a game on a 4K monitor at 1440p due to the very small performance difference and enable some anti-aliasing, or better yet (for now) just get a good 1440p monitor.
If you're in the market for an expensive gaming monitor and have an NVidia GTX600/700, then one of the new G-Sync, 27", 2560x1440 monitors might be ideal. You can Google Linus from Techtips (video), or "one week with G-Sync" (article) for more feedback.