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).
This post imported from StackExchange Physics at 2014-03-07 14:33 (UCT), posted by SE-user Luboš Motl