You don't lose hunger. When I first thought of this I thought it sounded too OP, but checked in /g just to make sure it was. Turns out players think this might be a good perk, since /heal has a cooldown of 60 seconds and it can be an inconvenience to keep using it. If you rule out this for a Supreme perk, consider it for an Ultimate perk. Also, while you're at it, you might as well remove /feed, since it is tied to /heal and /heal heals your health and hunger.
EDIT: Make it toggleable
EDIT #2: Disregard the remove /feed thing.