If you delete the app and re-install it after a short period, you might get notifications about new messages, without even having logged in.
If you delete an app, it keeps some important related stuff for a few days (about a week). Among other things — passwords and push notifications binding data. Maybe Apple meant that to simplify things for when you reinstall apps after you've deleted them for some reason?
Telegram has no idea that you deleted the app, so can't log you out unless you do it yourself — via logout or terminate the session from a different app. Otherwise you'll begin receiving notifications (if you did receive them before), if you reinstall inside this grace period that Apple gives you.
Naturally, if you wipe all data from the device using Factory reset (e.g. when you intend to sell your phone or give it to someone else), this will not happen.