I'm confused.
Are you asking if a 9 hour layover in Rome is enought to connect?
Yes. 2 hours would also be plenty.
On the customs question, yes and no. You do not clear passport control again in Athens, but you've already cleared it Rome. You don't clear customs in Rome, but you do in Athens. Confusing? It shouldn't be.
Why you would possibly fly from LA to Rome rather than Athens for travel time, when Athens is your destination, really boggles the mind. Travel time is negligibly different with a single connect somewhere in Europe. For example, you can fly LA-London on American and connect to Athens on BA. This should be very quick and efficient.