Apple Music Question

Hello,

First of all, this is my first posting so I am sorry if I'm not doing this correctly.

I am currently on the free trial of Apple Music. I recently got a new laptop and want to transfer my purchased music from my old computer to the new one. The thing is, when I imported all of the music into the new install of iTunes, the local library did not merge with the iCloud/Apple Music Library. If I download all of the songs from the iCloud/Apple Music library, will I not be able to play the songs when the free trial has ended? I do not have the money to pay for a full Apple Music membership (though it would be nice 😀)