I've got this installed on a few devices and push notifications come through straight away on all of them.
The problem I have is that periodically Facebook does something that causes this (and all Messenger versions up to 53.0) to go down. Something in the API must have changed in version 54.0 because that carries on working when everything below goes down. Sometimes this can last just a few hours, but most recently it quit working for over a week last month prompting me to post on here and on Reddit. It's extremely annoying as I'm using it on my daily driver (iPhone 5 on iOS 6.1).
Screenshot from last month's debacle: