I believe he actually is dead, but that Putin probably had nothing to do with it. Probably again a failure in their AA systems and they accidentally shot down its plane.
Putin has only to lose by his dead since if people think it's him Wagner PMC might now actually reach Moscow.
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.