From their docs, they do seem to have an emphasis on doing secure and private communications correctly. I would say that the only real guarantee that the org is practicing what it claims to be practicing is by having the code (which is mostly open sourced) audited.
In the US, there's really no such thing as secure cloud-based encryption in this manner (I believe I'm reading their docs right), because the US government could secretly coerce them to divulge their private keys.
They do, however, provide what they call a "Secret chats, end-to-end encryption" feature, which, if it's implemented as they suggest, appears to provide secure forward secrecy between two clients. It's unlikely that this feature would include some of the same fancy features of the larger telegram platform (it likely wouldn't support sharing messages across linked devices, though I could be wrong).
Before relying on something like this, though, I would probably wait for larger adoption and/or a professional security audit, as it turns out that actually implementing this kind of functionality can be difficult and prone to bugs which render security guarantees invalid.
For the mesh, we're generally looking for/interested in decentralized options. It doesn't currently appear that Telegram is offering the source for setting up Telegram communications servers, which would be the crucial routing hubs for all of these messages. If I'm wrong about that -- and assuming that the telegraph protocol handles multiple routing hubs -- this would be a terrific mesh service and would be a fantastic addition to a mesh server apps list.
Max