Can a locked phone's data be accessed when being repaired?
Anyone with physical access to the device can potentially do that. If the device was completely encrypted, that would be pretty tough to do (and hence really unlikely) – but all unencrypted stuff can be accessed. After all, you expect them to dis- and re-assemble the device – so put in easy terms, they could also "plug" the storage into "some of their readers" and copy all the content – no screen-lock or whatever prevents that. And a little more hardcore: those tech-guys should be expected to be able handling a JTAG device.

So the question is less whether it's possible (it perfectly is), but how easy and how likely it is. If you feel your data being more sensitive than your trust is high, that poses a problem.