No he does not, and above all, do not ask him to show his face, it tends to get him extremely annoyed because of it.

There are a few reasons (ones after the first are things he has mentioned on streams) actually:
1) he feels it takes away from the audio and the game by adding a facecam
here is is his quote to be exact: (Because I believe in what a homeless guy with a golden voice once said on YouTube. The power of radio. Audio is an amazing aspect of entertainment and I feel having a visual to go with the audio muddies the whole experience. Well, unless the visual is video games. Those are always awesome.)
2) Getting annoyed by people asking him about it too.
3)Legitimately fears some of his fans, DO NOT look up info on him, he has to buy a subscription to a service online that deletes his info yearly because of assholes doing that.
There may (unlikely) be other reasons as well, but I've been watching him for a few years now and these are the main issues he has with it.

EDIT: aww yiiss motha fuckin 69 posts.

Cry did a video explaining why he doesnt show his face. it said like he liked the mystery it has plus you can get to know his personality instead of just liking him for his look i guess

I also remember him saying that he prefers his private life to not be involved with work. Being in the public eye, you get a lot of haters and stalkers. I believe it was the BroKen podcast that had him touch on it.

You should focus on his actions and voice instead of his appearance. It doesn't matter because I love Cry's channel

No, he hasn't. But I'm quite annoyed by most of these responses because others seem making it sound like you care more about appearance, etc. You asked two questions and it's been answered, right?

no, his private life is what he treasures I think.

I never lose hope! Someday, he will!
But it's obviously his channel, his life, his face, his privacy, I could go on...
He shouldn't show until he' s ready, even if he'll never show.

I for one would be completely content with Cry never showing his face. It's been the laughs he's given me that I've enjoyed, not his face.