Thanks! I actually have another question. If I TT ahead one day to see if he's moving in, or to the next day after that, will it mess things up because Erik is still in boxes in the town I invited him from? Like, would I have to wait for him to be completely gone in the other players town before. I can go ahead one or more days? (Sorry for these questions—I've never done this villager trading stuff before~)
After you invite Erik and leave the other town, he is actually no longer in boxes there. Once a villager has agreed to move, when the town saves as you leave they actually move out. If that mayor goes to his house it will be locked up, lights out, with a "moved" message. He basically travels along with you.
So, yes, you can do whatever you want. Go ahead and TT for him if you like!