Hi. I know this is an aged thread, but one more reply wouldn't hurt

No, Telegram by itself is not fully anonymus. It is slightly better then things like whatsapp, viber and the rest of the shitfest but still not anonymous. As of not too long ago, telegram processes Law Enforcement requests, and will give info such as your phone number and IP to Law Enforcement agencies.
If you still wish to proceed, then there are a few ways to mitigate against de-anonymization.
1. Buy accounts - One way to securely use telegram is to buy acocunts from reputable sellers. I personally don't know any myself so i can't be of much help, but there are a hefty amount of sellers on this site (BreachForums) and xss.is, maybe even exploit.in. Once you buy a telegram account, you just drag and drop the tdata into your telegram portable and there it is. The ideal setup for this is a VPN on host OS (e.g Mullvad), and a windows 10 VM that is running through the whonix gateway (tor) and, optionally, another VPN on top of that even tho it is not needed.
2. Register and account - To register one, i'd strongly recommend using an Android Emulator that you're going to be running through a VPN + tor setup or an Android VM that you are going to be running through a VPN + Tor setup. As for the phone number, i use smspool.net (there are other alternatives which are better so please do your research beforehand) Pay with XMR (Monero) and use tor for more privacy and anonimity.
3. Final touches - Once you have your telegram account ready, there are a few things i'd do. first, set up a local passcode (make it something easy to remember), Setup a recovery email (I like to use onionmail.org or pissmail.com for that) and a password with 30+ characters. In case you bought one, log out all of the sessions which are not your own, that is is they exist. Setup a message deletion timer (1day works the best) and setup delete account after inactive for: 1 month. In case you do get arrested by adverseries, which if you followed this, you shouldn't, your telegram account and everything else will be deleted after 1 month. It's also best to implement some anti-forsenic methods. Disable automatic downloads from groups, channels, and DM's. All of this settings are in the telegram client.
That's about it. If you wish, you can just port your telegram account to whonix workstation if you really want to, but other then that, there isn't really much to do. Just be careful with who you trust

Hope this helps!