There are 24 muhly grasses native to Texas. We selected Muhlenbergia lindheimeri (Lindheimer's muhly) to do some research on, because, according to this USDA Plant Profile Map, it is native to Hays County. That does not mean that other muhly grasses won't grow in Hays County, or that Lindheimer's muhly won't grow anywhere else, it just gives us a known native to use an example as we start our research.
First, personally, we would say we wouldn't want to plant anything in late Summer in Central Texas. Both plant and planter could well drop dead in the heat and drought. But, we could find no firm confirmation of our view one way or the other. We did find, in various sources on the grass, the following statements on propagation.
"Propagate muhly grasses by seed or by dividing the root mass in the dormant season."
"Propagation: Divide plants or sow seeds in Spring."
"From seed, direct sow after last frost."'
We think the determinant is how much you want to plant. If you are covering a large area with the grass, it would probably be better to wait. If you are planting one or two clumps as ornamentals, you could do it early in the morning (mind the mosquitoes!), and then water. Even a drought hardy grass is going to need some watering early in its transplantation. This comes down to a use your own judgment call.