Don't worry about the heater core. It is not necessary. If the car came with no heater, or someone removed it, the hoses will not be there, and the in/out ports on the engine get pipe plugs installed. You can "bypass" it by connecting a hose to the two ports, but this does nothing. Plus, on your A/C car, there is a valve that stops the flow of coolant thru the heater core when you turn the A/C on. Same as having a blocked heater core, or no heater core.
I have a small valve on one of my heater hoses which I close off during the hot weather, to keep some heat out of the interior. The car runs no hotter, or cooler, with that valve opened or closed.
Now, this is not to say that the heater could not be used for additional cooling. If the engine was getting too hot sometimes if you ran the heater on full blast it could help to cool the engine a bit. But it is not part of the engine's cooling system under normal circumstances.
