As far as I know, supersymmetry has so many free parameters that is effectively not falsifiable. But it will be looking somewhat implausible, because part of motivation for supersymmetry is avoidance of fine tuning, and we need superpartners in the neighborhood of 1 TeV to avoid fine tuning.
Actually, Susy should show up pretty rapidly in principle after the LHC starts its run. Some people are speculating within the first year we should be seeing signals of the more plausible models. Identification of what exactly they are, will be hard and require a lot of time and effort, but there should be some activity seen nonetheless (anomalous signals of beyond the standard model physics)
5 years later, a non observation of a superpartner will definitely have people rethinking the electro weak scale dynamics and there are going to be some pretty hard questions to answer unless we see something else.
You can easily cook up a scenario where the LHC sees SUSY quickly, but has a hard time identifying it as SUSY as opposed to something else. For example, suppose the NLSP is the gluino, which weighs only a little more than the LSP, and everything else is heavy. So the only signature is an excess of events with a little more missing ET than they should have. Even establishing this as real is non-trivial - how do you establish it as SUSY?
Very hard. There are entire regions of the parameter space that are many to one with hundreds of competing models.
Its usually taken as a given that we'll have to get lucky for precise identification, or even that we could identify it exactly as a sign of supersymmetry/extra dimensions/insert model in the first place (absent a linear accelerator).
Still an anomalous signal is an anomalous signal, and everyone will pop champagne bottles if nature decides to ensure our job security =)
In 5 years or so, if LHC fails to find any superpartners, are ALL supersymmetric theories dead?
One thing that hasn't yet been mentioned is that even if the LHC (or ILC) conclusively rules out "low-scale" supersymmetry, there's no reason susy can't appear at higher energies -- potentially much higher energies, for instance with a susy-breaking scale around the GUT scale. In this case, however, susy would no longer stabilize the electroweak scale, and wouldn't necessarily be phenomenologically relevant (or even observable).
There are plenty of electroweak symmetry breaking mechanisms that leave open the possibility of supersymmetry at higher scales. For instance, I know some people (including Michael Dine, Mark Srednicki and Ed Witten) have looked at supersymmetric technicolor, though not much has been done with it (I imagine it gets really messy really quick).
At any rate, there can be supersymmetry even if it isn't relevant to electroweak symmetry breaking. Even if it only appears and very high energies, it would still evade the Coleman-Mandula theorem, and would be relevant for GUT model building and quantum gravity.
Large scale Supersymmetry still has many attractive properties for GUT model builders and theoreticians.
And if thats ruled out (say we falsify string theory and GUT models somehow), its doubtful it will go away even then.
Why? B/c if you really want to study a field theory in depth, and don't understand it, its almost always a good idea to supersymmetrize the action, which then lets you derive and calculate many hard problems that you previously couldnt. Its of course a different theory then, but qualitatively close enough.