Did you ever figure out the issue? I have a 2006 CS with only 62k miles and it does the exact same thing as you describe. I can't figure it out. I have replaced with new parts the following: all the coil packs and spark plugs, changed the intake manifold gasket, changed both MAFs, air filters and AC Compressor. It still does the hesitation when driving with the climate control on.
I bought a new throttle body gasket and throttle body cleaner. I'm going to try that tomorrow and see if it improves. I am not very confident it will work, but I will report back my results after I fini