Ah, Grasshopper! Very astute question!
Chlorine itself in the water is VERY acidic. Gas chlorination (don't try this at home) can drive pH through the floor!
The acidity of the chlorine in the water and alkalinity of the bleach neutralize each other! So it has zero impact on pH!

Aeration has to do with getting the CO2 out of the water... a little like making soda flat when it loses it...CARBONATION!

(ah the Great Circle of Life for us poolowners! )