I think you would need to use a different kind of flooring. I'm not an expert, but I don't think I've seen that kind of treatment done with carpeting.

Hi newcondo,
You don't need wood floors (in fact, wood floors aren't recommended with radiant heating systems since they don't conduct the heat well and potentially warp). Tile floors conduct the heat best, but carpet works too. Usually the coils are set into a concrete floor (i.e. a new one is poured over them), but there are other techniques as well. I'm not an expert, though we did put radiant electric floor heating into an addition we built. Here is a website with an explanation of how the different systems work:
http://www.energysavers.gov/your_home/space_heating_cooling/index.cfm/mytopic=12590/