I always get notifications about Telegram messages on my phone at around the same time (within a second or so) as I get the notification on the web client.
Currently Telegram keep working because it's get new backend IPs constantly via Google Play / AppStore services. Since push notifications are centralized they'll stop working as soon as application removed from stores so app wouldn't be able to get lists of unbanned IPs.
I always get notifications about Telegram messages on my phone at around the same time (within a second or so) as I get the notification on the web client.