As you know, semi-conductor photocatalysis can be initiated from the absorption of a photon which energy is higher than the semi-conductor band gap energy. This photo-excitation phenomenon allows the interband transition leading to the formation of electron in the conduction band and hole in the valence band.
The above described energy necessary for photoexcitation is directly linked to the material conductivity, meaning that an increase in the semi-conductor conductivity reduces band gap energy and thus allows photons with lower energy to be able to generate the electron/hole pair (in respectively conduction and valence band).
An exemple of a conductivity-related photocatalysis study :
Article On the electrical conductivity and photocatalytic activity o...
BUT, what should be noted is that after these charges generation, we expect them to migrate to the semi-conductor surface to initiate redox reactions. However, during this step, electron/hole charges may either recombine or be trapped before reaching the semi-conductor surface. These 2 phenomena are thus limiting the Photocatalytic efficiency and no direct informations about them are provided by the material conductivity.
Electrical conductivity of semiconductor depends on energy band gap of semiconductors. Under excitation ( optical/thermal) electron will go to conduction band leaving behind hole in the valence band. These electron in CB and hole in VB will contribute for the electrical conductivity.
These electron in CB and hole in VB will also contribute in photocatalysis which involve in reduction and oxidation and crests reactive oxygen species.