This paper thoroughly explored the fundamental interactions between cell association, cell load and throughput in a green (energy-efficient) small cell network in which all base stations form a homogeneous Poisson point process (PPP) of intensity $λ_B$ and all users form another independent PPP of intensity $λ_U$. Cell voidness, usually disregarded due to rarity in cellular network modeling, is first theoretically analyzed under generalized (channel-aware) cell association (GCA). We showed that the void cell probability cannot be neglected any more since it is bounded above by $\exp(-λ_U/λ_B)$ that is typically not small in a small cell network. The accurate expression of the void cell probability for GCA was characterized and it was used to derive the average cell and user throughputs. We learned that cell association and cell load $λ_U/λ_B$ significantly affect these two throughputs. According to the average cell and user throughputs, the green cell and user throughputs are defined respectively to reflect whether the energy of a base station is efficiently used to transmit information or not. In order to achieve satisfactory throughput with certain level of greenness, cell load should be properly determined. We presented the theoretical solutions of the optimal cell loads that maximize the green cell and user throughputs, respectively, and verified their correctness by simulation.