Yes you can reduce the thermal conducivity of materials by nanostructuring. This is one of the way of reducing thermal conductivity and get higher figure of merit ZT. This is because the phonons or lattice waves are scattered at the grain boundaries or interfaces or in general when the continuities of the lattice structure is perturbed.

I agree with Dr Chatterji in the fact that nanostructuring reduces the thermal conductivity due to phonon scattering by nanoparticles boundaries. It is less obvious that it will result in an increase of the thermoelectric figure of merit, as it is proportional to the ratio between the electrical and termal conductivities.

Size reduction can affect the electrical conductivity in two ways. In the same way it does with phonons, it can increase electron scattering rates, reducing the electron mobility. Also, as the surface to volume proportion increases,  it can also create defects that trap electrons, so reducing the electron concentration. Then, as regards the size effect on the thermoelectric figure of merit, the electrical conductivity decrease can largely compensate  the effect of the  thermal conductivity decrease.

Does it mean that reducing the size would not contribute to a significant increase in the  zT of the material?

I do not think that a universal behavior is to be expected. The electrical conductivity of different semiconductors can be affected by size reduction in different ways, depending on their bandgap, neutrality level, degenerate or non-degenerate character, etc.

One would expect the electrical conductivity of non-degenerate semiconductors (especially if they tend to form depletion barriers on the surface) to be strongly lowered by nanosize effects.  On the other hand, typical  thermoelectric materials like Bi2Te3 or Bi2Se3 are low gap materials, normally degenerate. Free carriers can effectively screen scattering potentials and nanosize should have a lower effect on the electrical conductivity.

Also both materials turn out to be topological insulators (TI). Topologically protected states at the surfaces are in principle less sensitive to scattering. The authors of APL 106, 053102 (2015) report an increase of ZT on nanostructured Bi2Se3, that they attribute to its TI character. According to these authors, thermal conductivity is reduced by nanosize, but the conductivity is improved by the increased contribution of topologically protected states at the nano-grain interfaces.

 In nano wire, reducing the diameter ,thermal conductivity is reduced greatly due to boundary scattering. In 2D supperlattice, which is the first demonstration that low dimensional material system could enhance ZT , phonons are scattered more by the interfaces reducing thermal conductivity.  If the internal interfaces of the nanostructured material can be designed so that phonons are scattered more than the electrons depending on the differences between their respective scattering length , thermal conductivity would reduce more than the electrical conductivity.  In general the presence of many interfaces which scatter phonons more effectively than electrons, results in the enhancement of ZT.