Depends on atmospheric conditions and how wet they are when you take them off. I don't really do multi-day hunts or hunts where I hike 5+ miles in a day so there are probably better people out there to comment, but in my experience if you hang them out to dry overnight on a night that isn't overly damp you can probably wear them in the morning assuming they're just a little sweaty. If they're soaked, like you stepped in a creek, they could take longer.
It will likely also depend on manufacturer. I have a bunch of alpaca socks from Pacas and Paka to a few local farms. They're all a little different.
I'd do a 3 sock rotation. The great thing about alpaca (just like merino) is they take a long time to build up stink. I wore some of my socks multiple times a week for about a month before they really started to stink. I think a three sock rotation could comfortably get you through just about any hunt.