It depends, but the odds are against it. Independence Air made the mistake of attemting to compete against United with an uncompetitive aircraft. For a regional-sized airline to survive, they'd have to find a niche market where the only other competition is like-sized aircraft or none at all.

Can a mainline airline survive global competition with a codeshare alliance? I think the answer is the same for similar reasons. A mutually supporting network of aircraft and routes allows an airline group to compete against other airline groups and are superior to stand alone airline systems. Even mighty Southwest can't compete in the international travel market from the USA to Europe or Asia. Eventually they might. If they do, it will be through codeshares.