No, an allergic reaction requires circulation. The perfume might diffuse into tissue and activate a few surviving mast cells, but the vasoactive chemicals (cytokines and biogenic amines) would have no real effect. Every sustained immune response I can think of requires recruitment of other cells (through circulation). Some tissue-resident phagocytes could maybe become activated through passive diffusion (although this is much less likely without circulation), but any effect they have would be *far* less damaging than the enzymatic reactions already taking place in tissue after death.