I say not.

Concepts like "queen," "male," and "female" are anthropomorphisms.

The drone carries the sperm (gamete) of his mother. He is entirely a creation of his mother. The drone has no father and can have no son.

Although the drone is functionally a male, the virgin queen is actually mating with the mother of the drone.

The entire order Hymenoptera (bees, ants, wasps) is one of the oldest insect orders and probably pre-dates the evolution of "male/female."