I'm a little confused here. If you have rings, why do you need to solder anything to the scope? German claw mounts which were soldered to the scope tube die not use rings, they used half rings, and the scope tubes were made of steel, which is not often the case with modern scopes.

Lastly, if you do decide to solder the scope tube, in my opinion all the optics should be removed first and replaced after the operation is complete.