It's probably possible to cross over HP and a superhero universe, but it would require some effort to make plausible. One version I read has it that if you use magic in public, you must give no hints that magical society exists, and the wizarding world is about as aware of superheroes as they are of, say, helicopters, and have sort of grudgingly accepted the existence of even the magical ones, because they simply don't have a chance of stopping Dr. Fate, but still want to remain hidden.
There's a few fics I recall that seem to go that route, to varying degrees, including the frequent 'the rules are different in America' thing. I may start a thread in the ideas forum for crossing over superhero worlds with HP.
Here's a couple examples, one silly, one serious, of fics that fit the concept above, to some degree:
<a href='http://www.fanfiction.net/s/2586094/1/Harry_Potter_Raven' target='_blank' rel='nofollow'>Harry Potter: Raven</a>, by Shadow Crystal Mage - if you're not familiar with his work, I'll just say that it's redundant to call this the silly one, even though it has very serious moments.
<a href='http://www.fanfiction.net/s/3243598/1/Wizards_Superheroes_and_Jackalopes' target='_blank' rel='nofollow'>Wizards Superheroes and Jackalopes</a>, by Willow-Bee the Cat. Despite the name, this one's more serious (as a side-note, it's one of the better-handled R/Hr pairings our there).