I had one bad experience doing this, and one good experience.
The good one was when the project was being graded off of external hard drives, so all I had to do was export the project (File:Export Project) & get the drives to the new guy. He imported my project file and had minimal trouble getting it up & running.
The bad experience, from months previous, was when I had to copy the media from my internal storage to an external drive and the new guy had me send him a backup of my database itself, but he never thought to ask for the project file. I don’t know if that makes a difference, or something got confused because of how the media was structured (the whole project was kind of a mess to begin with), but he couldn’t get the media to link up properly. Long story short, things didn’t work out well at all.
I think, and hopefully someone with more technical experience will agree, that even if you copy the media to a new drive it should go well if you provide the finishing location with the project file. But do it a couple days before so you’ll have time to troubleshoot if something goes wrong.