Installing cooling into an existing warm air system is often referred to as an "add on". Adding cooling 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 cooling only, but has the drawback of using the heating ducts to cool. These heating ducts may be undersized for cooling and will limit the amount of cooling that is installed. In an "add-on " situation, the heat gain calculation doesn’t matter as much as the parameters of the existing system. The cooling 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 cooling.
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.