Fire, Flashbacks, Electric Shock, and EXPLOSIONS are not things you want happening inside your home. However, everyday that you use a flood damaged heating unit you are risking one of these disasters under your roof. According to a GAMA, Gas Appliance Manufacturers Association, news release, gas, oil and electric control devices that are found on heating equipment and hot water tanks can malfunction if they are exposed to water. This can result in a disaster much bigger then the original flood that caused the problem. It is this fact that should convince you of the importance of replacing the units in the event that they become flood damaged.
However, it is also important to have a certified HVAC technician out to check the systems before you jump to any conclusions. Only a professional can determine the condition of the unit and deem it fit for use. If this does happen, you should then have that technician clean the units and replace any air filters. This will prevent the growth of mold and fungus inside the unit.
If you are one of the unlucky homeowners whose unit is beyond repair, you should replace it immediately. Water will cause the units to rust out sooner then normal, and would eventually have to be replaced anyways. Even if a system seems to be working well after a flood, it can fail at any time. You could either choose to replace now when the weather is warmer, or wait until the middle of a Chicago winter for the unit to conk out. The furnace or boiler is working harder in the colder months to keep the home at the desired temperature, and if it has damage, this is when it is likely to fail. The service technician you have come out will most likely notice the original cause of your problem: water damage.
Neglecting to replace the HVAC systems not only puts you in danger of being cold in the middle of a blizzard in Chicago, it also puts the lives of you and your family at stake. That is not something you should gamble with.