How to test production push notifications?

You can test APNS production environment building an AdHoc version of your App. The app will be using the production certificates and servers and it's purpose is exactly to test BEFORE you send it to AppleStore.

Take a looke at this link: what kind of certificate do I need to test apns using ad-hoc distribution?

The production push will work when you download the app from the App Store.

UPDATE:
You can also test the production push with an AdHoc build of the app; see Trinca's answer.

UPDATE:
Now, the easiest solution is to use Apple's TestFlight. (In TestFlight, it is easy to add new remote users, sending them an email invitation, they then download on whatever device they choose.)

Create an Adhoc distribution profile for your app in provisioning profile. Download profile and install. Choose the Adhoc dist profile to code sign your app. Archive ipa and save for adhoc distribution. Copy ipa to your device and test push. It will use production push certs as opposed to development cert. Hope this helps.

Testing production notifications (without releasing the build) is possible when the app is installed via Apple TestFlight.

This way the production notifications will be delivered to the app.

(If the exactly same build is installed via HockeyApp or by other means, the production notifications won't be delivered.)

Just set the build to internal testing after the build has finished processing in iTunes Connect.