The aeration from the SWG is conceptually no different than aeration from any other source such as waterfalls, fountains, or an air compressor. Technically, it is a rather efficient form of aeration since the hydrogen gas bubbles are small and they contain no carbon dioxide in them (initially). In other words, I would not consider having an SWG turned on as being slow aeration. On the contrary, it is quite vigorous which is why most users with SWG systems find a rather strong tendency for the pH to rise.
As for what happens when there is little aeration, in this case there is still outgassing of carbon dioxide and still a rise in pH, but it is much slower. In fact, in some pools it is so slow as to be effectively zero or swamped by other factors that affect pH. Of course, I'm assuming a hypochlorite source of chlorine in what I am describing since such sources are approximately pH neutral when considering addition and usage of the chlorine (obviously the pH goes up when chlorine is added and goes down when it gets used up so the timing of pH tests relative to such chlorine addition/consumption is important -- or put another way, measure the pH when the FC level is the same).
As for your question regarding having aeration happen quickly to prevent the TA from rising the answer is no. It does not matter how quickly the aeration occurs. The physical process of having carbon dioxide leave the pool water causes the pH to rise with no change in TA. It doesn't matter how quickly or slowly this occurs. The physical transfer of dissolved carbon dioxide, CO2 from the water into the air causes the following shifts to occur in equilibrium:
CO2(aq) --> CO2(g)
Dissolved Carbon Dioxide in Water --> Carbon Dioxide Gas in Air
H2CO3 --> CO2(aq) + H2O
Carbonic Acid --> Dissolved Carbon Dioxide in Water + Water
HCO3- + H+ --> H2CO3
Bicarbonate Ion + Hydrogen Ion --> Carbonic Acid
CO32- + H+ --> HCO3-
Carbonate Ion + Hydrogen Ion --> Bicarbonate Ion
Notice two things about the above reactions. First is that there is a reduction in hydrogen ion. That is, by definition, what causes the pH to rise since higher pH means a lower quantity of hydrogen ion. Second, notice that every component of alkalinity (bicarbonate ion and carbonate ion) that gets removed also removes a hydrogen ion. The definition of alkalinity is not only any substance that can accept a hydrogen ion (above a limiting pH of the alkalinity test -- around a pH of 4.5), but hydrogen ion itself is considered to have negative alkalinity (technically, it is the difference between hydroxyl ion OH- and hydrogen ion H+ that is the alkalinity from dissociated water).
This is confusing because we've always said that pH and TA move together. That is only true when adding an acid (adding hydrogen ion) or a base (adding hydroxyl ion or equivalently removing hydrogen ion). With carbon dioxide outgassing, we are removing BOTH a positive contributor to alkalinity (CO32-) AND a negative contributor to alkalinity (H+) that exactly cancel each other out (the carbonate counts twice for alkalinity and carbonic acid has two hydrogen each counting once towards negative alkalinity).
I know this is confusing. I'm not sure how to explain it any better.
Richard