I never quite understand this type of question. The Air Nomads clearly had sex with each other. Firstly cause they got 4 temples worth of people to populate, secondly cause 100% of them were airbenders (so high levels of cultural uniformity) and thirdly cause Bryke confirmed at a Comic-Con panel that the Air Nomads actually had a lot of sex.
Aang’s culture only seems to share the spiritual beliefs of monks (and be careful not to confuse Christian beliefs with Tibetan ones) rather than the physical rules. Not once during ATLA does Aang show any reservations of having a relationship with Katara because of his Air Nomad beliefs. While they might not have necessarily had the same type of relationships as the rest of the Avatar world, Air Nomads definitely had sex.
Interesting proposition. I don’t really have much case evidence to go on apart from maybe Aang’s relationship with Kuzon. If Aang had fallen in love with Katara they probably would have been allowed to be together but perhaps not in the temples.