This half armed mob has been staging raids and gathering arms for some time now. It's a bit more of a fight than what you are giving them. Even historically, protestors gave the Prussian military a run for its money. I wouldn't assume they'd be so willing to march into Berlin so soon, they will of course with time.I wouldn't be too sure of that.
The army had been very irritated with Fred Wm IV for his action in pulling the troops from Berlin when they were perfectly capable of restoring order had he only let them. Had that bit of foolishness led to his death, an awful lot of his officers - even if too diplomatic to say so out loud - would have privately felt that he'd got just what his stupidity deserved. They'd have led their troops straight back into the capital and "avenged" him with gusto - and a half-armed mob would have been totally powerless against them