I see. That makes sense. Is there any current gain with this base-collector conduction?
No current gain in this case. However, there's always a however

one can operate a bipolar transistor upside down, or inverted by swapping the normal Collector and Emitter terminals, so in this configuration there is current gain altho it's much lower than normal operation.
Long ago folks used this inverted configuration as a saturated switch since the saturation voltage is very low, sometimes below 10mv, where in normal saturated operation it's well above this. With modern FET switches this transistor inverted operation has generally been forgotten.
Best