Actually no, at the queen candidate thingy there were doctors to check the infertility quirkless_bakuhoe
Spoiler . . . . . . . . . Ppl told me that actually in the end they find out that the emperor was the infertile one, so if they assumed the queen was when it was him, it means that they did it
THIS IS MAKING ME MAD I'LL WAIT SOME CHAPTERS TO CONTINUE