Letting tap water stand for a period of time (24 hours depending on the surface area allowed for evaporation) before adding it to your tank will allow chlorine to evaporate, since it is less stable than cloromine. Chloromine remains stable in water left to mature and still need chemicals to neutralise. Chemicals introduced to negate chlorine and chloromine are designed to have immediate effect.
Airating the water before it is added will not negate anything else IMO...when you talk of other water parameters, are you referring to Ammonia/Nitrites/Nitrates etc? In which case (I would worry if you had ammonia and Nitrites introduced to drinking water) but NitrAtes can be...you will need to do a before and after check. My tap water has 10ppm Nitrates, my tank I keep at 20ppm bearing this in mind...I have not let the water stand long enough to realise any change in NitrAtes...
Check your water from the tap, let it stand for a while (24 hours) then check again..then you will know!
HTH