The compound is normally a solid, slightly soluble in water (1.23e-03 mol/L) with a very low vapor pressure (8.16e-08 mmHg) https://comptox.epa.gov/dashboard/dsstoxdb/results?search=DTXSID8032623 . Although gas sparging of liquids is a good way to remove dissolved gases, the solubility of this compound relative to its vapor pressure would indicate that the compound will remain in the water, increasing in concentration (unless absorbed in the soil) until the addition of make-up water.
As a plant hormone, I assume that the intention is to have it transferred to the soil with liquid water. Thus, if the aeration is intended to distribute the hormone in a water mist, it will be lost along with the water. If the roots are already in contact with the solution the aeration may be for a different purpose. As long as only water vapor is being removed, I would expect the IBA to stay in the solution.
It is likely that the product containing the IBA is a potassium salt of IBA. The aerator is immersed in the container which holds about 300ml of solution, and the plant is being rooted in that solution. No misting or soil. The H2O loss is due to the air being forced through the aerator and through the solution like in an aquarium. Thanks for where to find vapor pressure in solution, 8.16e-08 mmHg. I've got to play with this a bit before I mark as answer, but it is the result I had hoped would be the case.
It would seem that I would need to calculate the volume of air that passes through the solution per day to get some sort of effective volume to apply n=PV/(RT)? Ballpark airflow is 0.05cfm or 2.0m^3/day.