Eh, not really. They just do what their customers (the banks) want them to do. edit - forgot to answer your original question - simple answer, yes.
The Contracted Coin Terminals handle this on behalf of the Fed, receiving shipments from the mint and handling the flow of coins to/from the CCT's customers. https://www.frbservices.org/financial-services/cash/coin-terminal.html also https://www.frbservices.org/financial-services/cash/coin.html and https://www.federalreserve.gov/paymentsystems/coin_about.htm