I was looking for something else and found many articles, well above my head. They show that by recycling some of the dirty? exhaust air back into the cyclone you can improve the efficiency of the cyclone. I am not sure if they mean the electrical efficiency or dust removal efficiency or both. I would say it would allow a smaller blower for equal airflow into the cyclone but you would be inducing dust into the fan and causing more fan wear.
I have read of folks adding a blower into a air compressor to increase output measurably. If you can add 2psi to 14.7 PSi air I could see a significant increase. We are not talking crazy pressures like a turbo charger would use.
Bill D
https://onlinelibrary.wiley.com/doi/...ceat.200600085