Hi Sarah,
You can most certainly download music (or any other types of files) to your Android device. I'm assuming you're using the official Google Drive app? Here's how you can do it (quoted from a Help article that can be found [https://support.google.com/drive/answer/2423534?hl=en|here]).
# Open the Google Drive app.
# Tap and hold each file you’d like to select.
# Tap Download icon.
In return, you can upload music in your music app to google drive easily by downloading them as MP3 on your local computer first. One thing you need to keep in mind is that this is only for personal use, nor for commercial.
Hopefully this helped.