Do you mean electron transfer or excitation transfer (i.e. FRET)? 

Yes, we observe a typical example in bacterial photosynthesis.

Please compare, for example, rate of the primary and secondary electron transfer in the reaction center of purple bacteria such as Rps. viridis and Rb. sphaeroides:

https://www.researchgate.net/publication/232412761_Hystons_new_quasi-particles_and_electron_transfer_in_bacterial_photosynthesis

Article Hystons, new quasi-particles, and electron transfer in bacte...

If by "the rate decreases" you mean that the excited species now live longer, then the answer is yes. Often, charge separated species can live longer than excitons. This likely depends on the photo physical details of the system you are studying.

Also, Losytskyy raises a good point. Do you mean electron transfer or energy (i.e. exciton) transfer? In FRET, the donor lifetime will decrease (i.e. decay rate will increase) due to being de-populated by the FRET rate and instead the acceptor will be populated. The second process leads to an induction, typically of emission but more generally of signals associated with the excited state, of the acceptor. The acceptor excited state then has its own lifetime. 

So the answer depends on what you mean and what system you are looking at.