Judging purely from some of the theories of game design, a character such as that is likely to fail at being a relatable protagonist.
A lot of games create the 'mute' protagonist as a way of letting the player imprint their own personality on the character and others are wary to even attempt a serious portrayal of anything other than a hetero-normative male (with many noted failures at even that). A character such as the original poster suggested crosses a line in the sand that we still don't really even understand and probably a majority of people absolutely would refuse to try. There's a very real chance that some players would come to empathize and relate to the protagonist and upon discovering the big secret feel personally accused of something on which they have strong opinions and objections.
To be honest, just trying to find some answers on the cause of paedophiliac attraction, or its cousin disorders hebephilia and ephebophilia, appears to be a dead end with the current state of psychiatry. While there is a slight window of empathy towards a person afflicted with the disorder who has an unwavering conviction against acting upon such desires, the character will be demonized by the media if only to chase the entertainment dollar. If such a cause is discovered and can be offered alongside showing the protagonist to be a useful member of the game's society, I'd say it may have a narrow chance but is never going to be known as a mainstream hit.
(For the tl;dr crowd, you may start reading from here and decide if you want to go back)
There is, potentially, hope for this idea, but it's going to probably be decades and require a much greater degree of understanding (not to mention getting society comfortable with a lot more diversity in other types of characters and their real-life counterparts) before I'd evaluate this as anything other than game design suicide.
Now, given the hard analytical is said and done, there's a much simpler question to pose:
How does the character having this disorder in any way add to a fun gameplay experience?
A variation of this question applied to every element of a game is often an effective litmus test of game design.
Exploring personalities or experiences outside one's own can be fun but there's a lot of ethical responsibilities pertaining to portrayal that will need to be addressed. Unless exploration of the protagonist's world view or view of their self is key to the gameplay experience, it's technically irrelevant.