Three top ranking members of Wagner on the flight, Prigozhins main connection to the oil & gas sector, and Prigozhins body squad all on board, I doubt a mercenary army is organized enough to make an actual push without their leadership. You have to remember, a huge part of the Wagner ground forces were recruited from prisons and told "If you live 6 months on the frontline, you earn your freedom." I doubt most of the soldiers are actually loyal to Prigozhin, they just saw an opportunity for freedom from Russian prisons.