What Happens if I Don't Pay for Apple Music for a Couple Months?

yes

You lose access to the music you added from Apple Music as soon as you stop paying. Apple Music will keep track of the music you added to your library for 30 days after your subscription lapses in case you change your mind. After that all the music will be deleted from your devices/computers (if you downloaded the tracks). However, as soon as your subscription lapses you will no longer be able to play the music - even if it was downloaded to your iOS device or iTunes on your computer.