Temperature-dependent fluctuations of both site energies and electronic couplings are known to affect the excitation energy transfer in light harvesting complexes. Environment effects on such fluctuations as well as possible spatial correlations among them are investigated here in the PE545 complex from cryptophyte algae using ensemble-averaged wave packet dynamics to extract the exciton dynamics. This strategy directly uses the time-dependent fluctuations of the system Hamiltonian, as described by quantum mechanics/molecular mechanics calculations performed along a classical MD trajectory. Neither the fluctuations in the couplings nor spatial correlations including cross-correlations between site energies and couplings are found to be important in the exciton dynamics of the complex. This finding does not change if a polarizable embedding is used instead of its electrostatic counterpart. The impact of variations in spectral densities and screening of excitonic couplings based on the electrostatic and polarizable embeddings are discussed as well.