No - it technically dosen't get "carried on" but left at the door when you board. Take everything off that isn't part of the stroller, ie toys cup holders and fold it securely. We used a bungee to be on the safe side. The baggage attendant will bring it down and put it in the luggage hold after all the checked luggage has been loaded. Sometimes if they come unfolded and the person can't fold it (some are tricky) it can get damaged.
When you arrive the attendant will bring all the gate checked items, usually wheel chairs and strolers, up to the door for you to pick up. Usually its waiting but I have had to wait a few minutes occasionally for them to bring it.
When you get to the gate just check with the FA and get a gate check tag so the attendants can identify it as gate checked rather than sending it to the carosel.
TJ