In some situations, yes, though you'll still have a great experience.
so many people simply say "NO" but that's simply not the case. Look at the 1440p for Fallout 4 (which is hard on the CPU due to crappy, unoptimized code).
http://www.gamersnexus.net/game-bench/2182-fallout-4-cpu-benchmark-huge-performance-difference
(The i7-2600 is still quite good. In the above benchmarks your CPU would sit about 60FPS with the same other hardware and settings)
In most games you should get over 90% the performance of the newest i5/i7 CPU's. Even if you do drop a lot the FPS may still be high and if it's not simply tweak the game settings as appropriate.
Much of the time you'll have a GPU bottleneck instead. It depends on what GAME you are...