when making a claim with your CC insurance (for example AMEX, i currently dont have a primary auto insurance) for a rental car, does it effect you in any way?
I'm not sure I understand your question, but let me try.
The cc will cover as primary. AFAIK, if there was a police report written up, it will effect you in the long run (wgen you apply for auto insurance), but that has nothing to do with wether or not you claim cc insurance.
If the cc company requies a police report - that's where the effect would be.