No because they will just associate IP address and NAT port number. I'm sure the ISPs are keeping track of the NAT associations for this and other abuse tracking purposes.
That means there will be even more data to log to do this though. Many times the NAT will end up on a different port for different connections so you'll end up with something like 64k (assuming the CGNAT doesn't map under 1024) times as much data to log. It will make it harder and the companies doing the logging will have to have more information to narrow it all down.