Ken,
I will cut to the chase. The few minutes that you will be at a rest stop the a/c will be of little use as several have mentioned.
While traveling have all or at least two of the roof vents open and this should exhaust sufficeint hot air to make the TT livable.
Factor in the noise, short running time and hassle to connect and run,I really dont think that it is worth it. We stop often and take a break, I nap on occasion and it works great with no a/c. Note we live in S Louisiana so it is hot here, going and coming from the "cooler" areas of the country.
As always YMMV
Mentioned this to THE WIFE and she said that we have never encountered a TT with the genset and a/c running in a rest stop, MH's yes.
CCC