You need to do the event for Man to have sex with her. She can get preggers at any time before that from anyone that doesn't reset after the scene I believe. (So non bosses, mind you I didn't test Takumi)so question, do you need to do the yona x man event for yona to have kids or can you just get her pregnant without doing the event?
I imagine if you down her (through a fight) and rape her with man you could get the end result before the quest.