We have analyzed the dynamics of the upconversion-induced delayed fluorescence for a model multicomponent organic system, in which high concentrations of triplet states can be sustained in steady-state conditions. At different excitation powers, two regimes have been identified depending on the main deactivation channel for the triplets, namely, the spontaneous decay and the bimolecular annihilation. The excitation power density at which triplet bimolecular annihilation becomes dominant is the threshold $({I}_{\text{th}})$ to have efficient upconversion generation. The simple equation obtained for ${I}_{\text{th}}$ allows us to predict the theoretical efficiency of a generic system on the basis of few parameters of the constituent molecules.