I know two people who have done it. One moved here from CA, and my SIL when she moved from Utah. Both asked good questions, etc, and were very happy with the moves. SIL is still at her barn 5 years later.
"In the beginning, the universe was created. This made a lot of people angry and has widely been considered as a bad move." -Douglas Adams
BR, I have had great luck with sight unseen trainers.
When I moved my mare the last time, I had vaguely heard of the trainer and saw some random internet postings that sent chills up my spine (tween/teen girls gushing about how they'd date Dobbin if he were a boy etc) I called anyway and asked if he'd take her. It worked out fine. Sadly his wife recently died, but on the plus side, the teenage girl population has plummeted since the lesson program ended.
Over the summer, the mare went up to an Amish guy for a driving refresh. That also turned out well.
Ironically, the times I've done my homework, the barns I've picked have ended up being near disasters.