GSH, I don't know that there is a difinitive answer for you, but I'll throw some mud in the air and you can sort out what you can from it. I went to the office and pulled a pheasant hatching histogram from 1986. From the roadside surveys that year, hatching took place from about April 21 to August 19. This data is of broods seen in the roadside survey, so it may miss important survival data that would affect what was still living once the season opened. The disappointing part of the story for you is that only 0.6% of the hatch occured after July 31, and none after August 19. That isn't much, however, with the improved habitat conditions, their survival may well be higher than earlier broods.
A lot has to do with whether hens have already expended significant energy on earlier unsuccessful nesting attempts AND whether they have gone out of breeding condition already. Those birds will have a lesser to maybe 0% chance of bringing off a brood in the current year. Also, with pheasants, current knowledge is that once a hen has brought off a successful nest, she had a hormonal change that will end her efforts for further nesting. She will need to go through the complete seasonal cycle in order to be "reprogrammed" to come into breeding condition again. My best guess is that there is a limited chance of significant contributions from late nesting hens much beyond August 1. It is reasonable to think that any hen responding to the rainfall of the last two weeks would have little chance of surviving young come season. Such a hen would have 14-17 days of laying and 23 days of incubating to accomplish before chicks would hatch. That would put her well into September, well beyond where normal hatching has ceased, with brooding and accompanied risks for survival that are associated with that. I'm sure it happens from time to time, but to expect significant contributions from such an event would be unrealistic.