Yes. But they can also be in the clear depending on who does it and how they choose to license it.

If the performer doesn't mind and the work is public domain then it's an easy path

For example, here's the famous Waldstein by Beethoven performed explicitly as a free and open recording

https://commons.m.wikimedia.org/wiki/File:Ludwig_van_Beethov...

Funny apocryphal story about that song. For a long time I had got in my head that was extremely disruptive for the time. I envisioned men with powdered wigs running distressfully throughout the aisles as he plays the work for the first time as their wives fan themselves and couch faint in the seats.

I still think that every time I hear it and I think it's hilarious to imagine European high society losing their composure over this sonata. This and Brandenburg Concerto No. 3 are ridiculously close to modern music structure. That's a 110bpm breakbeat done with violins you're hearing.