Dunno if its for comic or TV Carl but for TV Carl - in the later seasons his arms were pretty damn hairy and he began to grow a small amount of facial hair, mostly a neckbeard. This wouldn't be possible for a FTM trans person to do without hormones which I don't think are easily available to find in the zombie apocalypse, nor would it be a primary concern.
For Comics Carl - He's like 7 when he first appears and thats pretty damn young to realise you're trans, accept it, come out to your parents and allow your parents to start dressing you as a boy.
Also for both Carls, he's been seen shirtless and he wasn't wearing a binder. So no. He's not.