Technically, the answer is no. But, if you’ve received a package and the designation is “locker” which is a common choice on a driver’s scanner, then they may have delivered the package to your box. Or if your package was SurePost which I’ll explain below.
I deliver it to mailboxes myself a couple of times a year. But, it’s only when the package fits and usually if the area around is giving the driver second thoughts about leaving it in the open. When I used to be a mailman they always made a big deal about how the box is postal property. And, even if you buy it yourself I believe it belongs to the post office.
I’m a little fuzzy on my memory there, so I may be miswording it.
Usually, your UPS driver is going to want to deliver it to your door. But, there is also a UPS program called SurePost like I mentioned before. Those packages are allowed to be delivered to your mailbox.. by your own mailman. Even if they originated from the UPS delivery system first.
You’ll be able to tell a SurePost package because it will show two barcodes. One shows the UPS tracking number, and the second shows the USPS tracking number. Good stuff.
Hopefully, this answered your question! Let me know if you have any more in the comments.