Anything is possible.. Chances are it hasn't been done, or even thought about.. The current changes are huge, and problably taking 100% of the devs time.
Trouble is, unlike the BGs you have to be at a specific NPC in order to que, and its on a timer, rather than a full time que, so youd have to add logic to move to the WG battlemaster 15 mins before the start of the battle, and when its over, hearth, and go wait by the npc again.
Well, couldn't someone who enjoys challenges get it working IF you are already in Wintergrasp? Something along the lines if you standing somewhere in Wintergrasp, queuing and doing battlegrounds, until the little box asks you politely if you would like to queue for wintergrasp, then it'd pause the battlegrounds and join WG, then rinse and repeat. Would that be impossible?