Rosguardia has hundreds of thousands of internal soldiers. Assuming their allegiance is to the MoD (and at this point there is no way of knowing), I don't see how Prigozhin could successfully stage the ousting.
If he was really trying to help the Ukrainians the most effective decision would probably be to attack the rear of the Russian lines to allow Ukrainian forces to come through. Wagner units have been off the front for about a month so I don't think it really has any effect on Ukraines ability to break through the lines without the above scenario happening, but nothing Prigozhin has said leads me to think he'd help Ukraine, as he also stated he plans to return to the Frontlines to help defend the motherland against the west after ousting Shoigu.
They're the type to freeze instead of fight or flight