Google Play Games: how long do XP and achievements last? If a game that uses the Google Play Games service disappears, are the associated XP and achievements removed from the Google Play Games' player profiles?
If by disappering you mean deleted app from playstore, No an app can't be deleted once published in google play store(Ref.). The "Delete" button only works for unpublished version of your app. It shoud instead be unpublished and  wont be displayed in the PlayStore results but the old users will continue using the apps and receive updates. See here


  When you unpublish an app, existing users can still use your app and
  receive app updates. Your app won’t be available for new users to find
  and download on Google Play.


And once an achievement is published it cannot be deleted (Ref.). But you can reset the players achievement's progress in the google play developer console or by using the Management API methods programatically only when the app is published.


  Deleting an achievement
  
  Once your achievement has been published, it cannot be deleted.
  
  You can only delete an achievement in a pre-published state by
  clicking the button labeled Delete at the bottom of the form for that
  achievement.
  
  Resetting an achievement
  
  You can only reset player progress data for your draft achievements.
  
  To reset achievements in the Google Play Developer Console, click the
  button labeled Reset achievement progress at the bottom of the form
  for that event. To reset achievement data programmatically, call the
  Management API Achievements methods... Read More


So that means the app won't be listed in the playstore results for new users but the game data will be stored for the users having installed the app before the app is unpublished.