Depending on which processor the stock cooler is from, it's possible that the CPU might potentially overheat and throttle performance under load.
Worth asking, what are your other system specs and what CPU are you upgrading from? Do you have an overclocking-capable (Z-series) motherboard, and do you intend on overclocking? If you are buying the processor new, the 7000-series processors are kind of expensive now that Intel and AMD are offering CPUs with more cores at any given price point. If you only wanted a quad-core, an i3-8350K performs virtually identical to a 7600K, and at least going by current pricing in the US, is priced low enough that you might be able to get the CPU plus a new motherboard for about the same price, if not less, than a new 7600K alone. Or there's the Ryzen 2600 for around the same price or less, which clocks a bit lower, but offers 6 cores with 12 threads.