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Yes, in effect you want the carpet and underlay to do the opposite of what they normally do. I'm sure I read an article at some point about all this when we were installing ours. Anecdotally our plumber told us to be really careful what we choose, he had recently installed a system under thick reclaimed wood, and it was apparently costing them the earth to get heat into the house. We went with LVT for this reason.
I thought carpet was bad for UFH? When we had ours installed, we were told roughly the order for best results was Tiles>Vinyl>Wood>Carpet, although there are some specialist carpets designed for UFH, and apparently the thinner the wood the better.
We have UFH but only on the ground floor, and buried under 6 inches of screed, so probably not an option, it is great though and would never go back, added bonus is that the cats and dogs love it, will spend the whole of winter lying on the floor rather than in their beds.