No, but he already shows signs of needing to breathe after a while. Him being on the moon showed he survived the impact of the attack that sent him there. Could he survive if he was just floating out there though??
The only reason he survives being sent to the moon and is able to go back to Earth is because he calculated a jump based on how the gravity affected a rock.. Might be looking too deeply into that small scene, but come on, he could've destroyed more of the moon or hit the earth too hard when he landed if he didn't do it properly.
I believe he's done punches that could send himself flying back..? I'm assuming he did at one point, if not, I'm wrong oops. But this only works because there's something to punch in a way. The air. (This might be a stretch, fair enough. I'm not entirely sure if physics would work like this for such a superhuman feat lol)
Space doesn't have air. So if he tries to send himself back through a punch, it wouldn't work the same way it would on Earth. Thus, he'd be stuck out there.. assuming he can be teleported or be affected by telekinesis. In which case, Saiki can also stop time or petrify him, then send him out there that way. That boy is far too OP in terms of ESP characters tbh