How big is the tank? If I understand correctly you have some kind of pass through for the tetras to go through but you don't think a Betta can? I'd be VERY skeptical about something like that as Bettas can & do try to through things that are too small for them then they get stuck & die or severely injured. As for the male being stressed, its always a possibility. I'd keep an eye out for color fading, nips or tears in his fins, lethargy, loss of appetite, hiding.