If the package you're shipping through USPS has already been paid for online for postage and the package fits into the drop off mailbox at USPS then yes you can drop a package in the USPS mailbox.
I've been dropping off packages in the USPS mailbox for a few years now since I sell stuff online though ebay and I pay for the postage online.
Then I just drop the packages that fit into the mailbox and if I have any larger packages I have to take them inside the post office and hand them to the postal employee.
Some post offices have designated drop boxes to place packages in that fit but you can also place the packages in the blue mail boxes outside the post office or near stores or anywhere else you see a mailbox outside.