No. Google uses its own proprietary music setup - even when you pin music to your phone you can't find/identify it.
So, unlike Amazon, you don't REALLY own it - you can just listen to it.
Sent from my rooted, debloated, deodexed Sinclair ZX-80 running CM 10.2 using Tapatalk 4
I stand (well, I'm lazy - I sit) corrected - thanks for the clarification.If you buy music from Google Play, yes - you own it. To use another player, you'll have to download every song from the Google Play Store and manage the files outside of Google Play Music.