Wrong! TTing back while they are in boxes will remove them from your town. This happens to over half of the villagers i was going to get from others and they say "Sorry! They got voided." Save your time and don't TT forwards. It ruins people's days like mine.
I can confirm that if you TT back to the day they're in boxes, they will stay in boxes. I've started my game up and (say I have a villager moving on the 25th), I check the time with one of my villagers with Isabelle and if it is past that day, I TT back to (in this case) the 25th.
I've kept a villager in boxes for a few weeks for someone before. c:
But keep in mind if you've loaded a character on a day past that date and go back, they'll already be gone. You just have to make sure not to load the game any day past their box day.