Yes, unclaimed packages are auctioned by the USPS. Much of what is auctioned, however, are insured packages which were damaged and refused. After the claim is paid, the postal service auctions off the packages to try and recoup losses from shipping insurance, as the USPS is self insured.

HOWEVER

The postal service has to make many,many attempts to either deliver the package or return it to the original sender.

If properly addressed, it is HIGHLY doubtful that a package is ever sent to auction.

There are many variables which go into how long it takes for something to get from one place to another. If you sent it book rate, third class, or parcel post, it can take time to get from point A to point B.