Does Music remember that a song is mine?

After I rip a CD of my own to Music and then Music uploads the music files to the Cloud, does Music later remember that the songs are mine? Does it even matter?

I ask because I used the "Remove Downloads" command on many songs and it wiped them from my disk -- even the ones that I had ripped from CDs.

The songs are still in the Music Library. If I now click the Download command and it replaces the files, will it know that they are originally mine?

I wonder because I'm looking forward to a time when I may not have an Apple Music subscription. I assume at that point, any music that I added to my library from Apple Music (but did not buy individually), will disappear.