Installing air conditioning into an existing warm air system is often referred to as an "add on". Adding air conditioning to a heating system involves the installation of an evaporator or cooling coil on the furnace, a condenser outside, and the refrigerant lines to connect them.
This procedure is less expensive than the installation of a separate set of ducts for air conditioning only, but has the drawback of using the heating ducts to cool. These heating ducts may be undersized for air conditioning and will limit the amount of air conditioning that is installed.
In an "add-on " situation, the heat gain calculation doesnt matter as much as the parameters of the existing system. The air conditioning must conform to the system rather than the heat gain figures. In many circumstances , these conditions are acceptable, but in two story buildings, it can create a problem. The second floor will usually suffer from a lack of sufficient air conditioning.
If the house is zoned floor to floor, with a thermostat on each floor, the effects will be minimized, but if the house has one thermostat and it is located on the first floor, the upstairs could suffer.
The alternative to this situation is the redesign and re-install of adequate ducts to the upper level. If these additional costs are not acceptable, at least be aware of this pending condition.