The usual protocol of a HE-stain contains a hematoxylin-solution with a pH about 3, a eosin-solution with a pH about 4-5. Sometimes also a differentiation step in HCl-ethanol.
Acid is known to fragment DNA, but it is a random effect, also influenced by time. I think the dye-binding itself is no problem, because it is reversible.
So my opinion is, that PCR may work after HE-staining, but it is not guaranteed. The amplicons have to be short enough (as it is also generally necessary for formalin fixed tissue).