Not necessarily, there’s a good chance that if Hitler took Moscow, Stalin and the Bolsheviks would have been removed from power, and a new government could have led Russia to victory, and both the Nazis and Bolsheviks could have been out of the picture.
Interesting thought. But I'd guess that had the Bolsheviks fallen, they most likely would have been replaced by a collaborationist government, something along the lines of Vichy France.
Very doubtful it would have collapsed the Soviet government. The capitol would have simply shifted eastwards to the safe zone. Napoleon burned Moscow. Russians had that in their institutional memory bank that loss of Moscow does not mean the government has collapsed, or that the invaders have won.