First of all, there are two different types of water hardness.
You have kH or carbonate hardness, which is the measure of bicarbonate and carbonate ions in the water. This is also known as temporary hardness. kH will affect the buffering capacity of the water and therefore, the higher the kH, the higher the subsquent pH as it becomes stabilized.
The second type of hardness, is gH or general hardness. This is primarily a measure of magnesium and calcium ions in the water. This is also known as permanent hardness as it cannot be changed by boiling the water like kH can. gH is what is being referred to when terms of "hard" and "soft" water are used as it applies to fish and plant life in the aquarium.
Now, to answer your original question about aeration changing water pH. Yes it can, by forcing off CO2, not adding O2 as others have suggested. This changes your kH readings and will help to buffer the water, resulting in higher pH readings. For the most part, this is good for the general health of your non-planted aquarium. As the kH and subsequent pH are raised, toxins like ammonia and nitrite aren't as easily absorbed into the fish's bloodstream. This is good.
I hope you find that to be useful.