Files can indeed remain after deletion. And there are many stories about bad apples in a repair shop doing this sort of thing.

What's the repair that's needed? In most cases, they'll need to turn your PC on & boot into the operating system to verify that the repair was successful. If you have encryption enabled, they won't be able to do this.

You might want to check with the manufacturer. The safest thing would be to not send your hard drive at all (in most machines, they're pretty easy to extract).