[Captain Moai]

You can switch from synthetic to regular, back to synthetic a million times. It won't do anything adverse to your motor, aside from running like dogshit on regular oil. The protection doesn't even come close. There's a very good possibility they underfilled your motor with oil and it may have had the briefest moment of starvation, or something to cause oil pressure to drop enough to cause damage to the turbo... but that makes little sense, seeing as the rest of the engine would also have been damaged most likely.

So yeah, on this one you're out. Grab a turbo, a turbo timer, use only synthetic oil and above all, never ever bring a turbocharged car to a quicklube place. Do your own changes or bring it to a trusted mechanic that will take the time to do it right. Be a pain in the ass and watch them every second if you have to.