It won't work.
Let me rephrase that, I'm almost certain it will definitely not work.
Look, my view on the issue is that frankly, it's a character with no support. As someone above me had posted, just because something is taboo doesn't make it deep or extraordinary, it's just a taboo. Right there you insure that it is a character that almost no one can relate to, and those that do won't say they relate to them because of the implications within that.
The simple fact of the matter is no matter how you play it, most people will get angry. If it's just mentioned in passing that they're a pedophile and not much else is called attention to it, then everyone would rightly complain that it's just arbitrary and pointless. If it's such a big part of them that the game evantually has us feel sympathy for the character, then everyone would rightly complain that they're sympathy could be taken by several news-media outlets as showing sympathy to molesting in general. To be perfectly honest, there is only one way I can see a pedophile being a protagonist in a video game.....they have to be hated at the end of the game. That's right, I put that out there, they must be hated. Why? Because you ask me what it means to be a deep character, it doesn't just mean someone who is different and it's their difference that makes them accepted by someone. A deep character is someone who's very nature demands that other characters and even the player must analyze and examine, a character who is not only not perfect, but actually has the risk of being hated. After all, who's to say being hated doesn't make you deep. Just look at several villans out there. We hate them and the chracter they represent, but that doesn't make them any-less deep. Hell, just look at James Sunderland. The man murdered his wife, and while we may beat the game well after learning that, we still have a hatred for James himself, even after we understand why he did it he is still someone we look at and say he was wrong, and that his actions are disgusting, but god-damn if he isn't a deep character then I don't know who is. But I know my idea of a pedophile protagonist who ends up being hated wouldn't work as well. Because someone somewhere will look at that and say that it is offensive to other pedophiles, that the story forcing us to hate the protagonist means that we will inevitably hate all with pedophilac urges, which can be viewed as discriminatory.
That's just my thought, and why I think that the first rule to any deep character isn't "Do they embody some social taboo" but rather "Can they be wrong? Can they actually be hated?"