If I'm understanding your question correctly, the aspirator is basically a one way check valve for the air injection. It allows air to flow to the port in the head but prevents exhaust gas from going the other way and into the air pump.
You will need to plug the hole in the head. It's connected to a passage in the head which exit into the exhaust manifold. If it's not capped, exhaust, and exhaust noise, will blow out the opening. There was an actual block off plate used at the factory on cars that didn't have an air pump.
The air pump was used to inject air (and it's oxygen) into the exhaust to burn off unburned hydrocarbons. The injected air raises the temp for combustion and also provides oxygen so the unburned fuel can ignite. If it had a diverter valve, there's also a tube and aspirator to the catalyst. Air is injected into the catalyst for the same basic reason, to increase it's temperature. Catalysts only work above a certain temp. Optimum temp is around 820 degrees as measured in the substrate (not the outer case temp).
For what it's worth, the p/n for the plate is 3751249 but it's long ago discontinued.