We have created an Android app, and we wish to share the APK with a few friends and family before publishing it to the Play Store. Our concern is that, if they install the APK, and then later we push an updated version to Play Store, even with the same signature, will the update be delivered to the users who downloaded the APK manually and installed it?
As of 2015, Google Play will detect apps with the same signature, but they will not be updated unless the user uninstalls the app, and then reinstalls from the Play Store.
So in short, to answer your questions - no, Google Play will not update the application if it is installed from somewhere other than the Play Store.
As of 2015, as stated in the answer by @Ankush, Google says it won't.
But in practice, if you sideload an APK, and an update is pushed on Play Store, it does get pushed down. We tested this scenario. It is important to note that the automatic update to the phone, will happen after a few hours of the app getting published (not APK upload) on the App Store, so in case you are testing, wait for 12 hours.
As of 20th Feb 2015, we have tested it, and this stands true.