Except helium doesn't seem to remain within the core. So the hydro-to-helium ratio would still be altered from what it was at the beginning.
I'm not aware of anything to suggest this. IF helium byproducts were distributed throughout a star, there would be no region of sufficient helium concentratiion in which helium fusion could take place in the later stages of suffciently large stars.
The only helium that should be present at the surface of the star should be that which was present in the primordial gas from which the star formed. Helium byproducts of hydrogen fusion remain in the central core of the star.