hmm... Looking at a teardown @ iFixit.com - the USB ports aren't on the logic board, but separate from the board, attached by a ribbon cable. If there is simply a mechanical problem on one of the ports, then the fix is just replacing that port.
And, the shop would not likely need to get to the internal storage just to test the USB port, and unlikely that the logic board would even be touched, other than a bit of work in that one corner.
Will the repair center need to boot to your drive? Maybe.
Do they have time to inspect all your files, making sure to copy off all your good stuff? Ehh - no...
If you prefer to be careful -- you have a backup (don't you?), and you could wipe your drive before dropping it off -- nothing wrong with being careful. Restore after you get it back - if you need to restore, that's why you have a backup.