My understanding is that, unlike phosgene, chlorine does not cause pulmonary edema for the very reasons you mentioned; turning into hydrochloride acid and burning the mucus membranes. Consequently it doesn't pass the bronchial passages into the lungs like phosgene and doesn't cause latent pulmonary edema.
But chlorine would be one torturous way to die that's for sure.
I inadvertently gassed myself once, was pool manager for a very old, very large pool built in the ‘20s with a fairly vintage chlorination system. Big baskets that you dropped “rods” of chlorine into. Had to be very careful not to drop them too quickly, no bubbles and definitely no splash which could get onto the other dry “rods” and create chlorine gas. One slipped out of my hand one day, all I remember was seeing stars, smelling what smelled like blood (salty, acrid) and out like a light. Not sure whether I’d be here if there weren’t two of us there, he saw it, covered his nose and mouth and dragged me out into fresh air.