I have a Razr Maxx (running the new ICS update 4.03), which comes with both the Google Play App and the My Music App. I actually prefer the My Music App over Google Play.
The Album Art Grabber grabs the art just fine and it updates Google Play but the album cover art does not show up in the My Music App. The odd thing is that it was working yesterday with six CDs I had on my Razr; it showed them all perfectly. But then I added more music today, used the Grabber to get the Art, all seemed to work just fine but none of the new stuff showed up. I cleared the cache and the data and rebooted the phone but no luck.
I would really like to be able to see the album cover art on the My Music App. Can you think of anything that would help. Note that the music is stored on the SD card.
Did you ever find a solution to your problem? I have a Motorola Atrix 2 with My Music and I'm having a similar problem with it. The Album Art Grabber did a great job finding all the art, but it's not being applied to my music files.