Hmmm... do y'all recall what happens if you let kalkwasser sit exposed to air? That chalky sheen on the surface: insoluble calcium carbonate that precips out and is useless and harmless.
Another famously oversimplified analogy by me
Really... this is best taken up with a chemist.
But still you can get my point, yes?
By aertating the effluent of a single stage Ca reactor heavily (or having a wickedly turbulent sump) you will indeed off-gas CO2 faster (good) and form more insoluble calcium carbonate (not good... or at least not ideal).
It may well be a moot point either way (small matter). But as a point of improving technique, I strongly recommend folks use a second stage media chamber on Ca reactors to temper the acidity rather than aerate or expose the effluent to heavy aeration/turbulence.
Its a bit of a balancing act here. You really want the effluent to be diluted (ameliorated... not aerated) into the bulk of the sump/system ASAP. That will minimize wasteful preciptitation... and that can be done without aeration and minimal precipitation.
Has that explanation helped?