Impersonators (James Cawley, too, I might add) seem to be in the realm of parody. However, that's not to say they aren't a cause for concern. But I think big IP holders aren't going to go after small potatoes Elsa's and Elvis's if they aren't making a lot of money. As with everything else, there's no value in going after someone with $63 in their bank account. Furthermore, there could be a huge PR hit if an IP holder did so. They would (most likely) just be interested in either people making serious cash and/or folks trying to build a future business based upon earnings from infringements. Sound familiar?
And Elvis impersonators seem to be a special case. I think the estate is more or less okay with it, since it's obvious there's no true brand confusion (unless someone records an album and then claims it's a 'lost classic'). Plus Elvis himself isn't really an IP. He may have been somewhat larger than life, but he wasn't conjured up by a writer or artist.