Naturally, if all the songs are clearly public domain, or your own compositions, the MCPS fee is not needed, but there can still be claims of infringement - look at My Sweet Lord (George Harrison, but claimed to be from He's so fine), or Fings ain't what they used to be (Bart, but claimed to be In the Mountain Greenery), to name just a few well known examples.

And Scarborough Fair (Paul Simon, trad song but Carthy's arrangement)