Can I convince someone else's villager to move in to my town if I have a villager that us going to move (they won't yet be in boxes if I do tell them to leave) Once they leave my town will have 8 villagers, unless I can get the other villager to move in before they do.
Yes, you can have 10 villagers at one time so you would be fine.
However, if someone was moving out while your town was full, you wouldn't be able to get any other villagers to move in until that villager moved out. Does that make sense?