The best way out here would be to HAVE 2 stages.
If you don't want it to react to user input interaction, the only thing you will need to do is not to set the second stage as inputprocessor.
Overriding stage.draw() would obviously work, but it would make it difficult to maintain. Moreover it'd be an undesirable design choice, since your game functionality is being described in a subclass of stage (it should be an actor (in an ideal world :D ) )
Hope this helps.