It's plausible. And if the outcome seems feasible and positive, why wouldn't they? Angry civilians outnumber the nobility and what assurance is there that every member of the military isn't sympathetic to the cause, should there be one. What are they going to do about it? Are you really wanting to find out what a people fueled by anger and a desire for a better standard of living (namely one where they don't have to be afraid of the person who supposedly calls the shots) can do when they decide that dying for something is better than living for nothing?