It will physically fit and you
can use it. But
should you? Personally, I
would not.
The i7-7700K has a higher 91W-TDP and produces more heat, thus, needs better cooling to dissipate such. The Intel stock coolers are less than mediocre and are meant for non-K Intel CPUs which has relatively low TDP (~65W), but, even then, the performance of that cooler is not great (noisy and mid-high temps). So, even without OC'ing your i7-7700K, you'd probably hover around high 60C - 80C/90C under load. Note that it won't damage your CPU, but it's really gonna be hot and the fans will be very very loud (pushes it to its limits).
If I were you, I'd spend a couple of bucks for a better air cooler such as:
PCPartPicker part list /
Price breakdown by merchant
CPU Cooler: CRYORIG - H7 49.0 CFM CPU Cooler ($34.99 @ Amazon)
Total: $34.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-08-09 21:48 EDT-0400