The ATS has the GM 6L45 instead of the 6L80, so the ATS is smaller, but supposedly somewhat similar.
My wife always uses it in automatic mode, 100% of the time.
For me, my experience is much like Tom0021: without the clutch, it just seems too much like an automatic to me, and I sometimes end up forgetting to shift. Therefore, I don't use the paddles very much anymore. However, I did use them extensively in the beginning solely for the purpose of slowing the car down/saving brakes on many of the steep hills we have here (similar to what Norm wrote above).
That actually brings up an interesting point. When she first got the car, on one of the "moderate" hills near home, if the car was in automatic mode and you let the car coast, it would soon go WAY too fast and the brakes would have to be extensively used. So, I started using the paddles there (and on some other hills) to help slow the car down with a downshift. After a month or so of that, I swear the car learned my driving habits. Now, when going down that very same hill, if you let the car coast in automatic mode, it will shift up to fourth, but WILL NOT go higher unless you hit the accelerator. There absolutely must have been some adaptive learning going on in the transmission controls because, in automatic mode, on that hill near home, it used to shift up to sixth and need braking, but now will hold fourth and need no braking at all.
Does the StingRay A6 also have something like this (learning) in its programming?