The Randall-Sundrum extra dimension scenario had been one of the most extensively studied class of theories. This offered a solution to the hierarchy problem. However, if this picture is not supported by the LHC, will it become completely defunct? What about theories like little higgs, composite higgs, technicolor, higgsless models (perhaps already practically abandoned?)?
If the LHC never discovers physics beyond the Standard Model (in its 1-decade-long career, roughly speaking), than sometime during its research – depending on the physicist (for some of them, the moment has already arrived, but those may be highly premature decisions) – there comes a moment when most physicists decide that the hierarchy problem is not solved "quite naturally" in the old-fashioned sense and Nature simply tolerates at least some fine-tuning.
This has the same effect on all the classes of models you suggested – and others. That's why it's irrational to single out one class of models that attempted to make the lightness of the Higgs natural. But many of these models, including Randall-Sundrum, still have other motivations to be studied even if they don't quite account for the hierarchy problem.
Even when it comes to the hierarchy problem, the LHC isn't able to "totally" show that Nature is unnatural. There are surely people, and I have always counted as one, who find 1-in-1,000 to be a tolerable amount of fine-tuning. So many physicists will still believe that new physics is "relatively close", whatever it exactly means, and their research will reflect this belief.