On devices with encryption enabled, can any apps start before the PIN is entered? On devices with encryption enabled that require you to enter a PIN before the device finishes booting, can any apps (including built-in ones like chrome or gmail) start before the PIN is entered?
If you are talking of Android N, then the answer is no, which uses File-based encryption and the following are enabled


  AOSP Dialer (packages/apps/Dialer)
  
  Desk Clock (packages/apps/DeskClock)
  
  LatinIME (packages/inputmethods/LatinIME)*
  
  Settings App (packages/apps/Settings)*
  
  SystemUI (frameworks/base/packages/SystemUI)*
  
  
  *System applications that use the defaultToDeviceProtectedStorage manifest attribute