Yes, lots of fish we can keep in aquariums are fish that are eaten by locals, such as gouramis and cichlids.
People in Florida catch oscars and jack dempsys and things all the time - fish that have been released and are thriving.
As far as North American cichlids, are you including Central America as part of North America?
I don't know of any actual US cichlids off the top of my head. Sunfish fill that role up here.