Personally i don't think they would care. I don't think the Queen expected it, and so the drones didn't expect it either. Once the Queen was dead, they got to what they were going to do out of instinct, which was to try making a new Queen. I don't think the drones would see a reason to fight eachother if one of them killed the Queen, i mean she's dead, what can you do? They're not emotionally tied to her, only mentally.