I'm fairly certain the most testing they do with used parts is clean them. I've used Emmots a few times and only had one bad experience. I thought my starter motor was dying, or the solenoid at the very least, as every so often all I would get was a clunk from the solenoid but no rotation of the motor. Emmots had one listed on eBay so I bought it. When it arrived it was a Marelli not a Bosch as I had but the fittings were the same so I just assumed LR had fitted either. Before fitting it, I tested it and found it didn't work. Solenoid didn't go clunk but the motor would spin with volts applied to it. As it was different to the one I had, I couldn't strip them and make one good one out of two so got on to Emmots and explained the problem. They immediately sent me a replacement, a Bosch this time, and told me they didn't want the Marelli back as if it was faulty it was no good to them. So they couldn't have tested it before sending it out.
Turned out there was nothing wrong with the starter though. The connection at the battery terminal had worked itself loose so I had a very poor connection between the battery and the starter and alternator. I found that out when the battery went flat while driving......