I would say no.
I found benchmarks to compared Skylake, Haswell, Ivy Bridge and Sandy Bridge 4.4GHz clock to clock in games with Titan X GPU.
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Clock to clock, 2600K would be up to around 32% slower in games if compared to Skylake 6700K.
http://www.eurogamer.net/articles/digitalfoundry-2015-intel-skylake-core-i7-6700k-review
32% slower in certain games not all and at lowly 1080p, increase the graphics load and that lead diminishes.
It's not as if the 2600k is giving unplayable fps in them select few games it's slower. Fact is for an CPU from 2011 it should be getting stomped on, but it's not and there is really no need to upgrade to to skylake for anything but benchmarking high scores.