The last time we had a drought like this in central Iowa was 1988. That one was worse. The lawns went dormant in mid-May and we did not get rain again until September. At the field day in 1988, several lawn care specialists asked about whether they would hurt turf by treating dormant lawns. To test this after the field day, All American Turf Beauty applied treatments to dormant turf ranging from normal rates to rates as high a 10 times normal. Our assumption was that we would damage turf with the high rates.
When the turf recovered in the fall, we were surprised to see no damage, even at high levels of application. We found that there was no risk of damage from applying the treatments to dormant turf and that the treatments had a positive effect in the fall.
So, in answer to the question about putting on the August round of treatments on dormant turf, I would say go ahead. I do not anticipate damage and will will have a positive effect when the turf does recover.
The articles below were from that time period. They are jpg's and you will have to click on them like a picture in order to read the text.