Telegram clients are open source. Whats preventing people from patching out ads out of their clients ?
I know only one: keeping the app running as a service, with all associated drawbacks. The app we develop (an XMPP client) does just that.
On iOS, it is not possible at all. To make an app receive messages and notify user about them, you must use APNS, and to do that you have to upload your keys to Telegram.