Thanks everyone for the responses! I should have been more clear in my post. The concrete would just be the base - there would be dirt or shavings added on top of that for scratching and such!
Still not good -- unless you're talking at least a foot of litter over the concrete -- at which point there's no point to the concrete.
In addition to the fact that chickens need to be able to express their natural instincts and my conviction that a lot of behavior issues that backyarders have are the result of setups that don't allow the expression of natural instincts ...
The ability of chickens to dig down to reach cooler layers of ground is a critical part of managing chickens in a hot climate. I make no interventions in re: heat other than to give electrolytes once a week when temperatures hit the mid 90's and have had absolutely no heat-related problems with my birds.
Part of this is that they are acclimated to my temperatures (the situation is different with chickens suddenly exposed to unusual heat than to birds who live in a hot climate), but I believe that their ability to pick a shady spot and dig in to spend the hot parts of the day in their little resting pits -- which are often so deep that that a given hen is down to the level of her back -- is one of the major reasons that I don't have to use ice, frozen treats, etc. to keep them healthy.
@U_Stormcrow, I know that you also make minimal heat-protective interventions in a climate very similar to the OP's. Do your chickens also dig in the way mine do?
For those of you with dirt foundation, does it help to have the concrete block footers or frame buried in the ground to prevent water from seeping in the coop?
The way to prevent water from getting into the coop is to pick a site with good drainage -- where water neither runs across the ground through the coop/run area nor pools in that area.
The money that you might spend pouring concrete would be better spent grading the site and, if necessary, installing French drains, grass swales, or diversion ditches.
A concrete block footer is, however, helpful to level the site of the coop and to make it harder for wood-eating insects and fungi to destroy your coop's base beams in our hot, humid, wood-destroying climate. It only needs to go below your minimal frostline -- probably only a couple inches.