Apple Music through Verizon

I have an Apple Music subscription through Apple- paid annually, loaded on a few different devices, with playlists created. I just accepted the offer from Verizon for 6 months free Apple Music with my mobile plan. Apple Music is now asking me which account I want to cancel, the one through Apple or the one through Verizon. If I cancel the one through Apple, for which I am paying, and keep the free Verizon one: 1) will my preset playlists still show up as long as I am logging in with the same Apple ID; 2) will the other devices (iPad, touch, other iPhone) still be able to access the original playlists?

I guess the question boils down to: would Verizon just be handling the billing, but everything else would remain the same?

thanks for any input.