Yes, but it is not easy. The problem is the file system used by Google Play for storing media files. Google uses some kind of coded file name that prevents other music players from identifying it as a music / MP3 file. Here is how I worked around this situation:
First you need a PC. Then login to your Google account on your PC.
Next, Google has a down loader that allows you to down load your music onto your PC. When you do this, the files are down loaded using a standard MP3 file naming format.
Last step. Connect your phone to the PC and copy the music files from your PC to your phone. Copy the files into the music folder on your phone.
Now you can start the Walkman app, refresh / search for music and Walkman should find them.
Hope this helps.