I had not thought about this aspect before, but it would make a difference if you added acid before or after heating the water if that water had high alkalinity.
Heating drives off CO2 from the water and provides minor alkalinity reduction by consuming HCO3. Acid consumes (neutralizes) HCO3 directly.
In the case of all the brewing water calculators that I'm aware of, they are using the laboratory alkalinity and that was determined from an unheated water sample. In the case of Bru'n Water, the calculation of how much alkalinity needs to be neutralized is based on that lab alkalinity value and that equates to a calculated measure of acid. If the water is heated first, a portion of that bicarbonate that you intended to neutralize with the acid will have already been neutralized by driving off some CO2.
Therefore, I'd recommend that acid should be added to mashing or sparging water prior to heating the water significantly in order to avoid overdosing the water with acid and driving the ph and resulting alkalinity lower than desired.
Thank you very much for the question. It was food for thought!
Enjoy!