Do you have to hand pre-paid thick envelopes to a USPS employee, or can you put them in the drop box?

I'm an Ebay seller and sell quite a few items on a regular basis. I use the USPS feature built into Ebay to print my USPS shipping labels directly through Paypal. So the postage is already paid on them. I use the typical bubblewrap 4 inch x 7 inch small cushioned mailers that you can buy at just about any retail store. I securely tape the pre-paid USPS label on it, and so far, I've been dropping them off to USPS employees at the counter. But my only local post office always has a HUGE line at it, because they are always understaffed. Can I put these pre-paid ones in the drop box for thick envelopes/packages? I've never tried it, and I was just wondering. However, I don't want to lose an item if that's the wrong place. Thanks.