Pretty sure she's had dialogue implying she would be quite ok with it, as they both have their agreement that it's ok as long as it helps grow the new airbending population, which she says is a possibility with MC. Just like how Tenzin has his swamp baby. Seriously she lets you finish inside and is all "so daring~"She'd never allow it. She loves sex but she loves Tenzin too and no way you're going to be able to NTR him.
One route have anything to do with the other? I'm just talking about the love route here.After the Tenzin that happened in Slave route though? No he's got his private bitch and is going to maintain his own harem of Airbender breeders.