In the traditional sense I think that if you asked most boat owners this question, they would have reservations about safety, and rightly so. For the most part they would not know about the Cobb BBQ but tend instead to think in terms of the traditional open BBQ, red hot to the touch and smoke everywhere.
My own boat is sixty years old, mahogany on oak, and the Cobb BBQ is used on a regular basis. I would probably not recommend the Cobb BBQ for use at sea, unless a Gimbal arrangement was in place. For anyone that doesn’t know what a Gimbal is. It is an arrangement that keeps a supported object upright with respect to the horizon despite the pitch or roll of the vessel. My own boat very rarely sees salt water and I never use the Cobb BBQ except in flat conditions or when moored, which answers safety concerns.
One of the beauties of the Cobb BBQ is that due to its design the outside (apart from the lid) remains cool to the touch. Also it is never normally necessary to use more than eight charcoal briquettes. This makes it very easy to light the Cobb on the stern deck and then, when the coals have turned grey, easily carry it inside to the galley. Another design feature is that when you start to BBQ, any juices from the cooking meat are directed to the side of the Cobb BBQ into a ‘moat’. This prevents meat juices from dripping onto the coals and the smoke typical of every other BBQ I know of, is absent.
If you do use the Cobb BBQ on your boat, like any other cooker, make sure that you have adequate ventilation. I fitted a six inch extractor fan to clear cooking fumes from my own galley. There is a double benefit to this. First of all any fumes caused by burning either gas (my other cooker) or the charcoal briquettes used by the Cobb BBQ, are whipped away. The second benefit of forced ventilation is that cooking smells are also removed. The size of boat I have is a comparatively small space and as we know, some cooking smells linger. Not now.
So back to the original question. Yes, the Cobb BBQ is safe to use on a boat, providing common sense and care is used. Safety should be a boaters’ main concern, but this has also to include things like not using open fryers and protecting ourselves and others from open pans that contain any other sort of boiling substance. The basic design of the Cobb makes it inherently safer than either of these other methods. I have also to point out that the Cobb does much more than just BBQ.