The distinction between populations is one of
- what fraction of nucleons are neutrons and
- how the nucleons are grouped (i.e. atomic species)
In the bulk of a neutron star nucleons are no longer grouped in atoms and find their equilibrium by transforming from proton to neutron and back again, so the naive answer is immediately "No, you shouldn't be able to tell."
Now we leave the part of the physics I am sure about and move on to the bits for which we really need an expert.
The important weasel word above is "bulk". As I understand it there are crusts of electron-degenerate (and non-degenerate atomic matter in a metallic crystalline lattice?) on the outside of a typical neutron star. If this crustal material does not exchange nucleons with the interior much then it might still retain some memory of the original composition of the star. In that case one can then ask how you could get access to that information, but at this point I am completely stuck: the process would have to be spectroscopic but we don't know much (anything experimentally) about the spectrum of materials under those conditions.
