So this thread has been very interesting and I should have explained why I asked the question. My friend Joanne caught a very, very small swarm a couple of weeks ago and they had a queen. We were surprised to find this queen in such a small swarm (just 2 medium frames of bees).
Placed into a small nuc we saw eggs last Tuesday and we were so happy that we had a laying queen. Then we were wondering if this could be a virgin queen and not a mated queen so we asked ourselves this question (Can a virgin queen lay eggs?. If she lays eggs of course they would be unfertilized.) So now you know why we asked ourselves the question.
But we will never know the answer because:
1. If they lay worker brood then of course she has been mated
2. If they lay only drone brood, then she could be a virgin queen who lays, or a mated queen who ran out of sperm
Anyway, thought you would like to know the reason for the question