I would be p*ssed if this happened to me tbh. If I heard, "Oh, I'm so tired," I'd be thinking, "boo-freaking-hoo! All you're doing is sitting there observing... ain't no way you get to go home and take a nap!"
Probably wouldn't care too much if not much was happening and he snoozed on the couch, but to LEAVE and go have a sleep? Sorry dude - if I'm having to stay awake AND be in pain, you're at least staying awake with me!
I plan to homebirth, so that will mean DP can go snooze if he wants... but he'll have to stay in the house. If he left because I was too noisy, I would rip him a new one, I think.