Photosynthetic reaction centres are pigment-protein complexes that can transform photo-induced electronic excitations into stable charge separated states with near-unit quantum efficiency. Here we consider a theoretical photovoltaic device that places a single photosystem II reaction centre between electrodes to investigate how the mean photo-current and its fluctuations depend on the vibrational environment that assists energy and electron transfer. Our results indicate that selective coupling to well resolved vibrational modes does not necessarily offer an advantage in terms of power output but does lead to photo-currents with suppressed noise levels. The exciton manifold and the structured vibrations assisting electron transfer can also support the emergence of a phenomenon akin to dynamical channel blockade, whereby excitonic traps can impose competing routes for population transfer under steady state operation. Our results help characterizing the device-like functionality of these complexes for their potential integration into molecular-scale photovoltaics.