Motherboard will 'support' it fine.
In terms of CPU, the 7700K is about the oldest CPU I'd even consider pairing with a 3070.
Yes, the 7700K will likely hold a 3070 back in some titles, at 1080p.
Less CPU intensive games, or at 1440p (or higher), the CPU will matter less.
Given the price for a 3070 (assuming reviews check out AND you can get one), I'd be comfortable enough pairing with a 7700K, at least initially - Although you should be looking at a platform (CPU/MB) upgrade next, sooner rather than later.