I never used Google music, but I have about 500 music files wma mp3 etc saved to my Acer C7. If google music lets you download songs you purchase, then I'd say it's a very safe bet you can save them to a chromebook.
You are correct in that sense. If the bandwidth is an issue, then I suggest a decent thumb drive, most are very cheap to acquire. Even a bottom 4gig drive will store hours of music. Just another suggestion.You do realize not everyone has an internet connection everywhere they go, or in my case, I don't have unlimited data everywhere I go. Constantly streaming audio from the cloud is a waste of bandwidth and precious data, especially when I/you can just save it locally. That of course, is just my two cents.