I wouldn't think the line snapping would be a problem, even if the break occurred relatively close to the bridle, especially if there were still some segment of the drogue in the water.
My major concern would be a wave coming over the stern and into the cockpit, which has occurred in the past with drogues deployed from the stern. Having witnessed a wave coming over the stern of a boat first hand, I wouldn't want this to happen to me. The boat didn't sink, but it came very close to going down, the cabin was rapidly flooded as was the engine compartment. Fortunately, the boat was quickly turned into the wind before the next wave struck, the bow kicked up violently, and the water in the cockpit rolled over the boat's low transom. This happened in Chesapeake Bay last year just a mile or two above Pooles Island during a brief, but powerful thunderstorm.
Now, in the above situation, it was a powerboat, but I would think the same rules apply. I'm still reading the above posted link and I'll make further comments when I'm finished perusing the text.