My estimation: short term it will fail.
Long term it will lead to substantial power movement.
Most of the young nationalistic russians are Wagner fans and despise the ordinary military, they view as corrupt and incompetent (which might be very true).
But they have been the fuel of the war. If Wagner is no more, or just a soulless hulk, this fuel is gone and moral will drop significantly.
And the current options for Prigoshin are
a) become a marty
b) submit to "justice" and public trial (but he knows this will likely not happen, but rather bullet or poison)
c) defect to Ukraine
He already made clear statements, that the war was wrong from the beginning, there was never a threat from Ukraine and the evil military commanders gave Putin wrong information. This sounds to me like building a bridge.
In either case, for the russian empire it is a desaster. And if it becomes a true desaster, there are chances it will become a disaster for everyone, as russian think tanks openly discussed the possibility of "preemptive counter nuclear strike". If they are about to die, they are willing to take everyone with them.
Mostly this is surely bluffing, as they made that statement, while they the internal power struggle was already ongoing as a message to the west: "don't exploit our weakness, we still have nukes". But partly I think it is a legit threat of cornered bullies.