Electric radiant heat on a slab with carpet is do-able, but you must consider a couple things:
Carpet, and padding are somewhat insulative. The thinner the padding, the more you will feel the heat. Also, use non rubber based pads as the natural rubber will break down with the constant heat, and turn to powder.
Slabs are an attractive, large cold mass for heat to travel to. Provide for an insulating layer between the Electric radiant heat and the slab.
This can be cork or synthetic acoustical isolation membrane, or a sandwich type "Blue board" with fiber re-inforced cementious facing (Google "Wedi board" to see what I mean)
Also, I have heard one report of the smell of the carpet being obnoxious when the heat was on. I have only heard of this once, but feel it may be worth mentioning if you have sensitive sinuses or respiratory problems.
Look for products that are tested by the TCA (Tile Council of america) and fully warranteed!