I agree with Konrad, I don't see why you couldn't. The only thing I would be concerned about though would be keeping the air pads stacked on top of each other throughout the night…
In winter I layer a ccf pad on TOP of my NeoAir. I have had quite the opposite experience as Bogs did when layering a ccf with an air pad.
After consistently using a 1/8" Thinlight ccf pad on top of my (original) NeoAir and having no problems, I decided one night to try the ccf pad under the Neo. I was immediately cold when I laid down and stayed that way. I laid still for an hour hoping that the Neo would soon warm up from my body heat, but it never did. After an hour I got up and switched the ccf pad back on top of the NeoAir. When I laid back down I felt immediately warmer, and it stayed this way throughout the night. After this experiment, I layer my ccf pad on top of my air pads when I need more warmth… If I only want to protect my air pad then I will put my ccf pad underneath.