OKHY... YOU WANNA THROW HANDS HUH?

An omega male would not be able to get a woman pregnant. Pregnancy in the A/B/O universe is decided via secondary genders in the case of Alphas, Omegas and Enigmas. Regardless of how dominant Dane gets with women, there shouldn't be the possibility of pregnancy, because I assume that a Male Omega's semen is impotent. However, in some other works, there have been cases of Omega males getting their beta partners pregnant during the former's heat, which is quite a bit of a stretch. Omegas, especially a dominant one like Dane, seek a partner who can impregnate them and not the other way around during their heat. Therefore, as long as this woman is also an Omega (since she would release eggs which would bind with nothing, because she would also be looking to get pregnant) or as long as the author does not consider an omega getting a beta pregnant theory worth any shot, I think we're pretty much in the safe zone. I do think that this incident will, however, spiral into Dane's identity being revealed as an Omega to the station workers, but I'm not too sure since I haven't read the novel.