Actually they not droop to protect stems, they curl to protect underside of the leaves and reduce the amount of transpiration.
Yes, they'll do good in Georgia with only difference vs North is that you probably will not get away by planting them in a full sun as we do.

I have two PJM Rhodos. One is quite large and receives much more sun than the other. Both tend to wilt easily in the heat and they are grown in a well draining sandy loam. The large plant has developed rusty red leaves under the current years growth. This has happened for the past two years. The plant seems healthy and has set many flower buds for next year. I don't know if the two plants are the same variety but the smaller one is growing in the shade of an 10 ft. tall Eastern Redbud. What could be causing these red leaves?

The red leaves on your PJM is normal. They turn red before dropping off.
Here's a picture of mine I took yesterday.
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