Shawn, that is an adept supposition, but it would be a rare thing, and SM is correct in that there would indeed be visible damage in the vicinity of the engines.
As you alluded; 'managing' (presumably shutting down) the correct engine would be crucial - there are enough examples where this procedure has been fouled-up even when the cockpit displays were blindingly obvious (or not .. as in the cases referred to!).
I would be keen if there was someone who could provide a brief overview of the mechanical (and other) factors which influence the onset of engine overspeed.