Find My Stolen Mini Mac After Installing New Clean Mac OS X Installation
I bought an iMac from a colleague - he wiped it completely and it was in the power up install process choose language.

Then as I continued the normal install it stopped as it thought it was stolen...

The serial number is checked against Apple ID’s and as it was still listed against my colleagues Apple ID it refused to continue...

Once my colleague removed it from his device list for his Apple ID all was then fine as I added it to mine.

So it may not work for them even if they do a fresh install until you remove that serial number from your Apple ID - at least that was my experience.