Not exactly. The Federal Reserve and the US Treasury do a dance where the Treasury tells the Fed how many dollars it needs and then creates notes, bills, and bonds in the desired amount. It then performs a simple asset swap with the Fed to receive reserves in exchange for those bonds. This is slightly obfuscated by the primary dealer auction process, but in extremis the Fed can and will just buy the bonds itself. This never happens because for some reason the private banks that are primary dealers don't choose to give away free seigniorage money.