I am a delivery driver for one of the previously mentioned.
I have delivered diapers to a few homes before but not as often as you'd think. Maybe once/twice a month. I don't think I've ever delivered to anyone ABDL, but if I have then they are good at laying low.
I generally look for boxes that could contain diapers and see who the shipper is. It's rare to find an unmarked box that could be diapers.
I only see obvious ones. I do deliver to a lot of medical related stops (nursing home, hospitals, etc) and they get a lot of diapers. The tough part is wanting to open the box and check out the product prior to delivery. I never have but damn, I am curious.
As far as picking up the boxes go, every driver knows what every daily shipper ships. End of story. The only exception would be if a shipper is so big that they require a semi trailor to pick up all of the boxes. From that point only the shipping guys and unloaders/splitters would know. Even still, it would be really hard to be a celeb and keep it a secret.
-I do know this, most delivery guys do between 100-150 stops per day. Your box is an obligation and a burden. They just want it off of their truck and could really care less what it might be. Youre just another stop in a really long day, so order freely and don't be concerned as to what the ups fedex/guy thinks.
Lastly, I live in my own delivery area and will probably deliver my own diapers to myself next week. I know that guy is a dl!