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
The worse of it all is the fact that for them to speculate that she's infertile, means the she did it with that trash