In theory this should not be possible (unless they put in a back door, but such a change is sure to be discovered pretty fast) because the messages are supposedly encrypted end to end using strong crypto, so the server doesn’t see the plaintext versions.
Obviously one must assume that anything based in Russia could be subject to State manipulation, e.g. Kaspersky antivirus but frankly how many people care? One could make the same argument for some US manufactured products e.g. it is IMHO certain that everything going via the Hughes-made Thuraya satellite gets copied to the NSA.
It might make it hard to organise our next fly-in to Russia 
Peter, the situation with Telegram in Russia is an absurdist play. The dialogue between the state and Telegram has been going like this:
– Give us the encryption keys!
– Sorry guys, it is impossible by design, there are no keys we could possibly give you.
– We don’t care, give us the encryption keys or else…
This is not the first time people in charge of telecommunications in Russia demonstrate their total ignorance of modern technologies. Or maybe they are just pretending to be so ignorant. Just like many other technologies, Telegram is quite difficult to block completely, and dedicated users will always find a workaround. The state’s attempts to block it will not thwart spies and terrorists, but they will make the use of Telegram very inconvenient for the general public, which may quite possibly be the real intention – that is, to silence the large-scale grassroots protest movement.
I imagine that Pavel Durov will be careful about where he eats or what door handles he touches :-(
