... should he? No, I don't think so. That would be shocking to the general audience, I think. I mean, fairy and Ernie interaction should be very limited, even outside of the show. I wouldn't suggest they be seen together in the daylight, but should keep any relationship they might have hidden to the public.
... I'm sorry, it's just a very unusual question. I don't see the relevance of it. I suppose if the topic is how would they get along on screen, how would they compliment each others comedic abilities, that's a good discussion, and would encourage the thread to continue with that.