In my mind, a C-Collar is perfectly appropriate if the GSW was to the neck. Besides stabilizing the C-spine itself, a collar would help hold your occlusive dressings and other bandages in place and minimizing movement that would dislodge them, aggravate the injury, etc.
For a penetrating trauma to the head, especially a GSW, if there was enough kinetic energy imparted to transfer to, and compromise the C-spine, well you're probably gonna have some eviscerated grey matter to go along with it...
Now since her we do have 5-6 providers on scene I'm certainly not going to stop you from putting on a C-collar for a head shot, well not unless it was getting in the way of airway management or something else similarly vital.. Now since collars and boards aren't part of our first in kit (unless the engine company is on scene first and asks us to bring it in as we pull up) I'm not going to sit around and wait for you to go get one to move the patient to the gurney and start moving towards the ambulance (though I suppose you could always put one on en route to the trauma center) ESPECIALLY when my county protocols on the matter state very clearly "SMR for penetrating injuries is generally not indicated and transport must not be delayed to apply SMR. Treatment of patients with penetrating trauma should not involve a backboard unless it is required as an extrication device or if there is a significant concomitant blunt mechanism."
Now as others have said, if your local policies and protocols say otherwise that you're supposed to collar and/or board this patient, that kinda overrides my opinion juuuusst a little lol