Yes, just like anybody else, the Fed can finance its purchase of something by selling an asset it already owns and using the funds to buy what it wants or it can incur a liability to pay for what it buys.
When the Fed literally prints money or when it credits deposits that banks hold at the Fed it is incurring liabilities for itself. But the Fed can also fund its purchases by selling assets.
As I pointed out in a post above, the Fed bought $58 billion in securities in the week of Dec. 4 and created only $4 billion in new bank reserves.
So, the answer to your question is no the Fed does not necessarily print money or create bank reserves each time it purchases treasuries.