How do you accompany other veggies with caramelized onions?
Carrots and onions have different cooking times, so no, you can't throw them together.

What I would do is cut the carrots as small as the onions (just for aesthetic purposes), start stewing the carrots in a closed pot first and season them as you like, and when they're nearly done, add the onions and caramelise them normally while they're stewing together with the carrots and you'll end up with caramelised carrot-onion stew.

Obviously, you can always cook them separately and then mix them just before serving, but that would take an additional pot and I don't like doing dishes...  ;-)