No the 8600k does not come with a cooler.
Also i give a downvote for the cooler you mentioned above. Its very cheap.
If you already get a "k" version of a CPU, which is overclockable, you should also get a decent cooler for it. Maybe look at a price range of 50-60.
If you have more money to spend, give the Dark Rock Pro 3 a look, or one of Noctuas.