I really think it boils down to performance. Christopher Reeve was able to distinguish Clark Kent from Superman purely with his mannerisms and physicality. You could believe that people would be able to separate the two identities from one another. I think what it really boils down to is an actor who can successfully separate both identities.
Someone who could give Clark Kent their own character traits and quirks and create a Superman persona that is confident and far removed from the Clark Kent personality. I think, with the right actor, such a balancing act is possible.