Do I need an HVAC vent in this bathroom?
I'd say maybe you don't, if it doesn't have any exterior walls, which it does, so that's a yes. 

Drywall is the enemy. This is also a good time to upgrade any of the electrical on the interior walls as well. You're two steps from a gut job; go for it.

As to whether you need more registers elsewhere, I don't know; I'm not a math wiz: calculate the heat load and the corresponding ventilation requirement (that's the part i pay for).