An assembly for an aircraft propulsion system (20) includes an engine core (26), a bypass duct (58) and a bleed circuit (102). The engine core (26) includes a compressor section (48), a combustor section (49), a turbine section (50) and a core flowpath (90). The bypass duct (58) includes a bypass flowpath (60) outside of the engine core (26). The bleed circuit (102) includes a bleed passage (112) and a flow regulator (114) and is configured to direct bypass gas through the bleed passage (114) from the bypass flowpath (60) into the core flowpath (90) when the flow regulator (114) is in an open position. The bleed circuit (102) is configured to cutoff gas flow through the bleed passage (114) between the bypass flowpath (60) and the core flowpath (90) when the flow regulator (114) is in a closed position.