I would expect that the alkalinity of the water would increase rather than decrease as the dissolved CO2 is released.
When water has CO2 dissolved in it, IIRC, some amount of carbonic acid results, though I'm not sure how much. The acidity of the water should decrease as the CO2 is released, unless I'm thinking about this wrong.
I don’t know the chemistry (though I should), but I can tell you if you need to lower the alkalinity in your pool the easiest way to do it is to raise the temps and aerate. What you also find out when you own a swimming pool is that there is a tenuous connection between alkalinity and pH. They are related but not directly. We often have a 200+ Alk reading and a pH of 6-6.5 at the same time, which technically would seem to be impossible, but I can attest to the fact it isn’t.
For years we tried to balance that out by adding Bicarb or borax to raise the pH, but would end up with an over the top Alk. reading (less so with the borax). Then we would add acid to bring down the Alk reading and the pH would plummet. Since learning this little secret of heat and aeration we have brought the Alk. down from close to 230ppm to 100 or less in 3-4 days without adding chemicals and without screwing up the pH.