I think it depends on the cat. For Miya, it was a surprisingly easy adjustment--in that I mean, there were no accidents involving bodily wastes and she was eating fine. On the other hand, since she wasn't used to all the people, she made it a point to have three hiding places that she knew would make her mommy a little irritated. Eventually, I just stopped trying to get her from hiding under the beds and just left her there until she wanted to come out. I also kept all her toys from our old apartment so she could have something that could remind her a bit of the old place.
For a long time, gettings things in order in the new place took some time and Miya didn't like that too much, but she decided to take it in stride and mess up her toys, too.