As in you don't think he can be sickly comedic and dark? Taking a look at his many roles, I think he's got quite enough experience in both to provide for a pretty good choice as the Riddler.
Didn't you just describe the Joker? I guess most of my experience with the Riddler character, is from the 60s TV show, and second the Silver Age re-prints that came out back in the 70s. I think the Riddler's main problem is that he was secondary to the primacy of Joker and the Penguin. He most likely is following the Catwoman's steps. But I think his sense of humor is more mainstream. He wants to have too much fun, and his ego is so puffed up that he has to leave clues to his schemes.
If anything I would say the Riddler is the antithesis of the Batman's entire universe. He is light and airy, while everyone else is dark and scary. So Johnny Depp would need to be channeling Harold Lloyd, a kleptomaniacal Groucho Marx. Puns not bombs, or something like that.
But...as I am not directly paying the salaries, or doing the hiring, I am just going to hope for the best. They seem to be taking care of the franchise a lot better than they were 10-15 years ago.