You can, but it will require you to reflash you motherboard most likely.
Flashing your motherboard is pretty painless, and not nearly as dangerous as it was in previous years - you have a back up UEFI if anything should go very wrong.
the i5 6600 has a locked multiplier, but because of the way skylake was engineered, you can increase the baseclock, or BCLK, to get a pretty wicked OC.
Your OC potential is huge, the 6600 should be able to push 4.3-4.5GHz before you start becoming unstable.
If you go into your UEFI and you don't see an option to increase BCLK then you may have a motherboard with a UEFI version that had it removed (at the request/demand of intel). If you don't have BCLK as an option - search for a Z170A-X1 UEFI with BCLK enabled, there are plenty of resources for this - it is a popular board.