My boat has a Factory installed onan 6.5KW gennie. I have a question. Lets say I am anchored out on the lake. Will the generator running keep the batteries charged when running a stereo system with amps? I know its designed to run the a/c unit, etc.

The boat has a built in charger, but I believe it charges the batteries at 10amps, which Im sure the stereo system draws more than that. New to the whole generator thing. Thanks

I don't see why not. Just because it is only charging at 10 amps doesn't mean the batteries can't keep up. I suppose if you tried to run it maxxed for several hours you could have an problem.
Running the AC is a whole different animal, that is the same as being on 120V shore power.