Do extra-dimensional theories like ADD or Randall-Sundrum require string theory to be true? What I mean is could it turn out that the world is not described by string theory / M-Theory, but that nevertheless some version of one of these extra-dimensional theories is true?
I have no real background in this area.  I just read Randall and Sundrum's 1999 paper "A Large Mass Hierarchy from a Small Extra Dimension" (http://arxiv.org/PS_cache/hep-ph/pdf/9905/9905221v1.pdf).  Other than the use of the term "brane" and a couple of references to string excitations at TeV scale, I don't see much about string theory, and I notice their theory only requires 1 extra dimension, not 6 or 7.
 A: Extra-dimensional scenarios may be described as "inspired" by string theory but they are independent hypotheses and they may be true even if string theory is not. However, one has to reduce the ambitions and standards of consistency.
Sociologically, it's surely true that the research of models with extra dimensions has been adopted and pursued by many people who have never take studied proper string theory or taken a course in it.
Despite the academic independence, a confirmation of experimentally accessible extra dimensions - which is extremely unlikely to occur, due to their likely tiny size - would be a huge evidence supporting string theory because it's the only framework in which the extra dimensions actually have a justification (many).
A: Well, we have to answer another question first: "Is there any complete or consistent theory of quantum gravity which doesn't arise from string theory?"
Constructing RS models and ADD models is "phenomenological model-building".
A: In 1974 String theories are shown to require extra dimensions. An object similar to the graviton is found in superstring theories.
However these alternative dimensions or realities must be exactly the same as each other, even to the last grain of sand. For example There can not be different version of you in those universes, they must exactly be the same. To explain why, one must consider the butterfly effect, any small change can lead to large changes, leading to completely different worlds containing completely different contents. So you and I are unique to this  universe alone or there are exact copy of us in other universes, much like effect of two parallel mirror
