You can sort-of do this, if you have them sit down then type /logout instead of going through the menu they'll stay sitting down.
You can do the same with sleeping on a bed and other emotes, but I always find it difficult to get the /sleep emote positioned correctly so they're the right way round and not hanging off the bed, and it ends up taking more time than it's worth. It's easier to have them sit down and imagine they'll go to sleep later.
Oh yeah I know it can work, but when the end result is making the few seconds I'm logging out a bit more immersive I don't want to spend any longer than necessary getting it right or have to do multiple attempts and adjustments because it defeats the point of doing it at all. I'd rather do something which has a similar effect and reliably goes right on the first attempt.
It would be nice if they made beds interactable like chairs are, so you just have to push a button to sleep on the bed and it puts your character in the right position automatically.