the idea behind the air pump at least, is that its an exhaust gas after burner, and that's even what its called.
The additional air injected at the exhaust ports ensures that any unburned hydrocarbons do end up burnt somewhere along there route out the tail pipe. Unburned hydrocarbons are very, very bad to human health and the environment.
On catalytic converter equipped cars, its essential for this pump to be working, along with lambda control or the cats will not operate correctly and or clog.
the system fitted to your car attempts to do the same sort of thing, but without a pump, the act of the exhaust gas passing over the air injection ports sucks in fresh air so that the afterburning effect can still take place.
as far as driveability is concerned, there will be no noticeable difference, even on air pump cars they require very little energy to operate when working correctly.