In a NOT gate circuit, does charge not flow through both the transistor and output line when the transistor is "on"?
You are correct for the most part, but what you have here is essentially two switches that are working in inverted states. 

If you drive the base of the transistor then you will draw about 29mA collector current from V1 and force, assuming saturation, the collector to be about 200mV (Vce sat). Current would flow through the diode if the voltage at that node was sufficient to forward bias the PN junction of the device, but that is not the case. So, what happens here is that when the transistor is ON, the diode switch is reverse biased (off), and when the transistor is OFF, it provides a high-resistance path (an open) and current will flow through the two series resistances and drive the diode.







simulate this circuit &ndash; Schematic created using CircuitLab