I don't know about donation boxes, but I have used one of the phone kiosks for an old broken phone. The thing scanned my drivers license and had a camera like an atm.
All phones have an identification number usually called an IME, so when they gather the phones they collect the IME and there is a centralized database system to run the numbers against to see if they have been reported lost or stolen. So I think the phone would have been discovered if someone went that route and they would be on camera using the kiosk.
Just a note, I used to manage a cell phone store for a different major retailer than sprint and people would come in all the time to try and activate a phone they had purchased from Craigslist or ebay and they wouldn't be able to because it was on the national lost or stolen list. If you ever buy a phone from one of these places ask them for the IME so you can check it yourself and make sure it is clear to use. Their ate a few free websites now that allow you to do this. My life tip for the day