Google Music will stream your music, and let you mark music as available offline, so it will download it to your device. I have unlimited data, so I wanted to test how much data I can use in a month, so I allowed it to sync some music over 4G.
If you click on a song and make that available offline, it works fine.
If you click on an album and make it available offline, that works fine, too.
If you click on an artist, things don't work like you'd expect. You would think that all songs by that artist would get synced. Instead, what it does is grabs the Album name off every song by that artist, then syncs all the albums. You'd think that would be ok - but Google Music doesn't handle missing ID3 tags very well. If you have even a single song without an Album tag, it will come up as the album "Unknown Album". With me so far? Problem is, there's no special treatment for that album name. If you tell Google Music to download an artist that has even ONE song that has no album listed, it will download EVERY song by EVERY artist that has no album listed.
Good thing I'm on the unlimited plan, still. There is no way to cancel a download, or remove it from the download queue, You just have to let it download, then delete it. I could see a hypothetical situation where somebody on a tiered data plan (and not near wifi) really wants a local copy of the music from one artist. Say, the night before they are flying somewhere and plan to use their phone as an mp3 player on the plane. They figure "I only have like 5 songs by that artist, I'm sure that will be fine". They tick the box and hit the hay. They later discover that it downloaded a few gigs of random music.
My major gripe with Google in general is that there is ZERO customer support. There is no place to report bugs, make suggestions, or receive support. I won't bother trying to report this to them, but I thought I'd warn people here just in case.