As has been established in other answers, Google's Play Music program does not support files in ALAC. However, the M4A extension is used by several supported formats so Play Music will attempt to add these files to its library. Unfortunately, when Play Music actually tries to play these files, it causes errors. One solution (mentioned above) is to re-encode the files into a supported format.
If you want to keep ALAC files on your device for use by other players, you will need to prevent Google Play from seeing your ALAC/M4A files. After considerable research (and a fruitless exchange with Google Support), I discovered that Play Music will respect ".nomedia" files. When a .nomedia file is placed in a folder, the media scanner will ignore (recursively) that folder. While there are several techniques for putting .nomedia files in place (e.g. this list), StudioKUMA's .nomedia Manager is by far the easiest.
WARNING: While this approach is able to hide the ALAC files from Play Music, it may hide your ALAC files from the player you want to use. In my case, Rocket Music Player provides the option (1) to limit the library to specific music folders and (2) to ignore .nomedia files in those folders. This combination (for me at least) allowed me to keep and use my ALAC files without breaking Play Music (which I use to access older MP3s synced to the cloud).