If you are using the Signed version aka Non-rooted, you CANT CONNECT to your Google Play by any means. Signed APK are non-login version while Unsigned APK able to do that BUT at cost of root your phone which means risk of malware and virus from non-trusted sources.
If you still confused about that, ask the Admin in this site and do PM with him about what is Signed and Unsinged APK in detailed version.