Technically, the USPS claims they can.
As a practical matter? No. They would simply send a Be On The Lookout note to each postal facility that the mail could have gone to, but those are mostly ignored and only if someone runs across it and cares about it will it resurface.
Never send anything you care about by USPS without a tracking number. I’ve heard stories of carriers and employees trashing mail if it doesn’t have a tracking numbers.
Really? It gets photographed.....the carrier better have a good explanation on where that piece of mail went ....if it shows up on the scan and not with the customer ..