If your hand fed boiler cannot be shut down by closing all the incoming air, then, yes you have a combustion air leak.. The fire will not shut down instantly, it will take an hour or two, depending on the size of the bed of coal.. but you should be able to shut it down, or at least drastically slow it down.
Many circulators have an internal, inaccessible 'flow check'. It's a spring loaded plastic plug in the outlet of the pump that has to be pushed open by the circulator's water pressure and flow. These flow checks are intended to prevent 'ghost-flow' and uncontrolled heating of zones.
If you have pumps with intern flow checks, and you want to have gravity-flow when there are power outages, you need to either remove the flow checks.. or plumb a loop around the pump, and put a ball-valve in the loop. Open the ball valve when you want gravity flow, close it when the pump is to work normally .
If you have zone valves, they will [should] have either manual levers to open the valve.. or it will be a 'fail-open' design.
You need a system where the less dense hot water can rise, and the cooler, denser water can sink, replacing the rising hot water.. this is gravity flow..
IF you have to pump water down hill, like into the basement floor, or into a zone of baseboard units, it won't gravity flow, the heated water must be able to rise above the boiler's level. Very large diameter pipes help gravity flow, small pipes won't flow as much or as fast. I've been able to heat a home with 3/4" copper baseboard zones very well during a week-long power outage.. This was years ago in my first home, with a natural gas fired boiler.
I'd get as suggested an IPS, and add several large car/truck batteries to the system.. It's just a matter of stored current. The larger batteries will last that much longer.
Or, a back up generator. Which is what I have to have in my current house and buildings.. almost all of my heating is via hot water heated floors or baseboard zones. But my heat source is out in the back, and it must have a circulator to get the heat into the house.