No. Intel's new K-series processors do not include a stock cooler in the box. There's not much point in buying one if you aren't going to overclock (in that case get the i5-6500 or i5-6600 instead), so you'll need a cooler better than that anyway.
So because of the ending "k" it does not contain a stock cooler, but if it was without the "k" it would have, correct?
Correct. The "K" means that it is unlocked (can be overclocked), but for their most recent gen of CPUs (6th Gen, AKA Skylake) Intel has stopped bundling stock coolers with unlocked CPUs.