The door switch is there to prevent the blower from sucking in vent gasses and circulating them through the house. The suction created by the blower can be stronger than the draft created in the vent. If the furnace is operating in an enclosed space and with the blower door off, the fan can literally suck vent gasses out of the vent. This can cause two problems. One, the negative room pressure can interfere with the furnace getting enough combustion air, and two, the vent stops working – dumping combustion gasses into the room. This creates a situation where carbon monoxide can be created, dumped into the room, picked up by the blower and circulated through the house. This is especially true for furnaces that get their combustion air from space in where they are installed.
What about sealed combustion systems which draw combustion air from outside through a PVC pipe? Although the combustion air for a sealed combustion furnace normally comes from outside via the PVC combustion air pipe, if you remove the panel to the burner compartment, the furnace will be pulling air from the surrounding area. More to the point, the vent gasses could conceivably be pulled out through the burner area. Although not likely, if both panels are off it is possible for the blower to create a strong enough negative pressure to interfere with the combustion process even with a sealed combustion furnace.
So after working on a gas furnace make sure the door switch is functional before you leave. Do not leave it jumped out or mechanically defeated. You do not want to be responsible for a tragedy.