Even if the luminosity dip ends up being so far out of the ordinary that it totally upends our understanding of where the star is in its life cycle, and even if we were to determine that it's going to blow "soon", that would just mean it could blow any time within the next few thousand years or so. The outer convective layer isn't in direct contact with the core, and the dynamics of the two are decoupled on short time scales.
Because the last burning stages happen so quickly (from thousands of years down to days, depending which stage you're talking about), there's no way to know how far along things are in the core after the carbon-burning stage (or thereabouts, I forget exact details, and a quick trawl through Wikipedia didn't refresh my memory on the relevant points) except by neutrino emissions, and except for the supernova itself, you won't pick up enough neutrinos to get workable data unless you're close enough to be fried. (Actually apparently for the closest supernova candidates, which aren't anticipated to fry us, neutrino astronomers have some hope of picking up thermal neutrino emissions during the silicon burning phase, which would give about a day's warning. I don't know details, I've just heard it mentioned offhand).