You certainly can; just make sure its copyright has actually expired.
While you’re free to add fresh arrangements of public domain songs to your Songtrust account, it’s important to confirm the original work’s copyright expired or its author(s) explicitly put it into the public domain beforehand. For instance, “Deck the Halls” is a traditional Christmas track you could tweak and register as an arranger, not the composer or author. Also, make sure to check off the box that asks "Is this work in the public domain?" within the Song Registration page.
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