What effect will blocked flue have on the boiler?

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.