The combustion air will not be able to go out the chimney. Since it has to go somewhere it will leak out the boiler into the boilerroom. If the boiler is air tight the pressure inside the boiler furnace will become high enough that the air will surge or run backwards out the forced air fan. This could lead to combustion outside the boiler, explosion or at least filling the boiler room with smoke and poisonous gasses. The flue on our gas fired hot water system once became jammed shut. It was the smell of incomplete combustion that alerted me to a problem. If it had happened when everyone was asleep or no one was home, the house would have filled with carbon dioxide.
Soot and carbon should not be building up in a gas boiler, if they are then there is not enough air getting in and the boiler will be inefficient and may be producing Carbon Monoxide, which is very dangerous. You need to have the boiler checked and Serviced by a qualified, state registered gas fitter. If the boiler can be repaired, the fitter will also clean it for you. Quite honestly, trying to service gas appliances yourself is a very dangerous, risky thing to do. If you get it wrong you could end up killing yourself and your family. In the UK it would be illegal for you to do this yourself (see related link below).
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