No. While both the HRSD and Chesapeake charges appear on the same bimonthly bill, the Chesapeake rate structure is separate from HRSD charges. Those will still appear on your bill at HRSD rates.
Chesapeake's bill covers the treatment and delivery of fresh drinking water and the transport of sewer to the HRSD sewer transmission system. HRSD charges you (their current rate multiplied by CCFs used for that billing period) for wastewater transmission and treatment.