Yes, you understood it!
When you have your TeamSpeak Client installed, press Control+I to enter Identities Options. On there, select desired identity, right-press on it and select “Export”, then save it somewhere safe and copy it onto some USB thumbstick.
On a new computer, or a freshly installed Windows, install TS Client, press Control+I again and in there right-press on the left side of said window and choose “Import” option, then select your saved file. Your identity will be back.
Additionally, create myTeamSpeak account and log in to it inside TS Client.
To do this, press Alt+P, enter myTeamSpeak tab and at the top either press “Create Account” or put your credentials in proper places and log in. Additionally, check “Stay logged in on this computer” window to not worry about anything.
Next, enable synchronization in a tab below login and select “Automatic”.
After that, your identities will backup on myTeamSpeak servers and if you ever have to reinstall WIndows, just install TS Client and log in to myTeamSpeak account and everything will be back, including your server groups as well.