If he means the electrical connection to the contactor, then probably nothing. If he means the air conditioning tubing connection to the condenser or evaporator coil, then you will eventually have a failure and the refrigerant will leak out.
Evaporator coils are made of soft metals that conduct heat well. Aluminum, Copper need steel plates to hold it all in place. Most often the steel will rust first and then corrode the copper later. It could be several years before it leaks refrigerant, or yesterday
If the rust is actually caused buy an older style drain pan, ... does Noah ring a bell?