The following information is regarding TuneCore's Publishing Administration service
Yes, provided that you create a new arrangement of a public domain work.
Currently, the duration of a copyright in the United States is the life of the author plus 70 years after their death. Once this time has passed, the work falls into the public domain and is no longer protected by copyright.
However, if a song’s lyrics and music were published before 1926 then the song is in the public domain in the United States. For example, the traditional Christmas carol “Deck The Halls” was published in the United States in the 1800s. If you have created a new arrangement, you are able to register this song as the arranger but not the composer/author.
It’s important to note that a song may be in the public domain in the US, but not in another country. Plus, you need to be certain that the version you’re using is the one in the public domain. Other people may have created new arrangements of a PD work and that specific arrangement may not be in the public domain. The bottom line is you need to do your research!