Yes, because Wagner are mercenaries. They don't give a flying fuck about politics, they're there to do a job and get paid.

The actual Russian Army has literally resorted to conscripting randomers and criminals to try and boost troop numbers - I'm not convinced many on the Russian side of the front line are there for ideological reasons. From what I've read, the people who believe in the Kremlin line are basically the Russian boomers and older who are going to die off in substantial numbers over the next decade. And Russia is probably going to get substantially poorer over the next decade as the world accelerates the transition over to green energy and the brain drain continues to neighbouring countries.

Once Putin is dead, the head of the snake is cut off and there'll be a period of chaos where all the potential successors start playing their hands to try and seize power. Once someone seizes the mantle, they'll have a much easier time of things if they're focussed on consolidating power internally rather than trying to do that and simultaneously manage a war, so I reckon it will be called off pretty quickly.