Yes, it DOES stop showing you as online. If you are not sharing your last seeen/online status with somebody, he will NOT see you online, regardless of the app they are using.

There is one exception to this: people will see you online for a brief period of time right after you send THEM a message (otherwise it would feel like talking to a wall).

See: https://telegram.org/faq#q-can-i-hide-my-last-seen-time And: https://telegram.org/faq#q-who-can-see-me-online

Good to know