Need to replace bad converter.. Can I do this?

Will I still have regular power if I'm running the generator, with the 30 amp plugged in to the gen?
(like to run AC and wifes hair dryer?) ..
I know, I know.. hair dryers aren't real camping.. LOL

Then just run the lights off the battery when the generator is off ?
...keeping the battery charged as needed when the generator (Champion 3100) is running?

Thanks again~