The carpet alone here is not the problem...like was mentioned earlier, if it is a low-pile, very dense carpet, it would probably be fine. The bigger issue here is the combination of carpet AND concrete. First of all, is the concrete flat? Can you get a good check of it with the carpet in place? If it isn't flat, how do you plan on leveling with the carpet there?
And forget flatness...how about potential moisture from the slab and the hardwood manufacturers' warranties regarding slab preparation-- I don't know of one manufacturer that will warranty their product floated over a slab without a vapor barrier under the hardwood. That means you would have to put 6mil poly or something like it over the carpet. So, now you have carpet pinned between a concrete slab and a vapor barrier, and the carpet will be holding whatever moisture is being emitted from the slab....that's potential for lots of problems--mold,mildew, delamination of the carpet backing, release of the adhesive used to hold the carpet down....
Long story short....I wouldn't advise it!
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