Yes, I have gone from reporting to CMO to CCO back to CMO. My background is in CS and Account Management, but I'm a marketer at heart so I find value in both, but goals will definitely shift depending on where you sit.
As far as any cross-over, generally speaking I view CM as producing 1:Many programs to drive retention and growth at scale, where as CSMs are 1:1. If advocacy is also your responsibility, this is a great position to help ensure customers are successful so they become advocates.