Does the Google Play app always updates automatically?
According to the Section 3 of the Google Play Terms of Service you consent to Automatic Updates:


  Updates. You may need to install updates to Google Play or related Google software that we introduce from time to time to use Google Play and to access or download Products. Products originating from Google may communicate with Google servers from time to time to check for available updates to the Products and to the functionality of Google Play, such as bug fixes, patches, enhanced functions, missing plug-ins and new versions (collectively, "Updates"). By using the Google Play store and installing these Products, you agree to such automatically requested and received Updates. 


*Bolding added for emphasis.