I think these possible extra dimensions are likely existing at energy and length scales that are probably not reasonable to probe "directly" (we don't observe much of anything "directly" anyway if you think about this twice but let's not go there for now) the corroboration or falsification of these "constructions" are entirely in its implications.
What we are dealing with here is an abduction of "best explanation". If a theory that makes use of actions based on dynamics in higher dimensional spaces are the best explanation then that is all i ask for! Anything objections beyond that borderlines old times realist objections that i see are not helpful.
One need to discuss what is "best explanation", but that will het the thread off topic, but i consider this question relevant and tightly related to understanding the landscape problem (in GENERAL that is, not just the "string landscape"). Also it can not be the fuzzy occams razor or "beauty" silly arguments, i think we actually need a technical and physics basis for SELECTION among "best explanation", on par with fitness of organisms in biology.
Now if string theorist want to claim large extra dimensions that should show up soon at more reasonable energies, that's an option in theory maybe. But as string theory stands today it seems that's a possibility only, so falsifying a possibility does not falsify the program. This is of course the problem.
So as I see it, the most realistic chance to support or disprove ST in the, is to solve the landscape problem, and try to make some explicit predictions. In fact even without new physics at LHC, I would personally be MORE THAN please with if string theory could "just" postdict the standard model, and thus reduce the number of free parameters ;-) Thats the job of the string theorists, not ours :) But it would not quote be enough to show that the standard model is a "possibility". But they haven't even identified this possibility.
I am not even sure if there is some proof withing string theory that the landscape MUST contain the standard model + GR? Ie. an existence proof, without necessarily finding it. Does anyone know?
So from my perspective and interesting in this field, while new physics at LHC would be exciting and fun, we have more than enough work to find a consistent coherent picture of current physics. One might argue the point in doing that, ie why would a coherent theory be "better" than a patchwork of theories? I see many reasons for that, some of extend way beyond physics and connects to AI and brain research. So there is no lack of potential spinoffs.
/Fredrik