Can I make Google Play not run a background process (on CM10)?
I think Google Play is bundled with some services that requires for another applications.
 ie : Applications that uses Google Cloud Messaging (GCM). 

According to this link: http://developer.android.com/guide/google/gcm/gcm.html


  GCM requires devices running Android 2.2 or higher that also have the Google Play Store application installed....


So basically, Google play is not there only for install a new app or check for updates etc.. So I think it's better to leave it as it is.