Drones are haploids so probably nothing. I suspect you'd need the full chromosome set to get the full developmental effect of the royal treatment.

Given that when a hive goes queenless the workers start laying eggs including in the royal chambers they're desperately building, and since the workers are unfertilized all of the eggs are haploids that hatch into drones, it has probably happened many times throughout apian history. No drag queens have been spotted.