Yes. It's important that you're working within the confines of 'public domain'. Public domain works are considered those where copyright has expired or author(s) explicitly put these works into public domain.
Example: you record an arrangement of Deck The Halls – a Christmas song in the public domain. You will be able to register this song as the arranger, but not the composer/author.

Please note that most PROs pay out performance royalties at a reduced rate for arrangements of public domain works.

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