In principle yes. However it depends on the sensitivity of the thermopower to impurities. I think that with ppm you will see nothing, with some at.% it will be possible.
you may think of Mott's equation on the Seebeck coefficient, where it relates energy band structure variations near the fermi level to the thermoelectric power. The band structure nature could depend on the separation between the atoms that forms alloy. But, the direct relation between lattice parameter and Seebeck coefficient is a trivial way to achieve....In this context, I also need suggestions from experts.
I´m not sure if you get a direct connection between the lattice parameter and the Seebeck Coefficient. An direct impact of the cyrysal lattice on the Seebeck coefficient might be hard to see since the density of states and the charge carrier mass in the system is changed aswell since your adding a additonal chemical potential.
In Addition if you add some Donoratoms it might be possible that you get a Fermi Level pinning throught defect states within the bandgap which is well known for transition metal sulfides.
Article The effect of the band edges on the Seebeck coefficient
In principle resistivity and its derivative to regard to energy: the thermopower are function of the scattering of electrons on ionic sites near the Fermi energy.
The scattering depends on the electron-ion potential. If you replace an atom by another (impurity), the interaction potential is not the same. The scattering depends on the relative position of atoms. Thus the lattice parameter may have an influence. Temperature through the vibration of atoms has also an influence. It changes the probability of finding an atom at a given distance from another one. The change of distance under the effect of temperature (expansion), of pressure (contraction), or the swelling due to atoms with a larger size may have influence. The electronic transport properties depend also on the number of occupied AND of vacant states near the Fermi energy. This is characterized by the Mott g factor.
If, in principle all these effects have an influence on electronic transport properties, it does not mean that these effects are always measurable.