Will my project source most of its current from the battery?
The 5V power rail can only have one voltage at a time.
If the console voltage is more than 0.6V above the 5V power rail, current will flow through the diode until it isn't (0.2V if it's a Schottky diode). If it's less than that, it won't.
Since the 5V power rail is directly connected to the battery, the voltage on the 5V power rail is always equal to the voltage coming from the battery.
You do the math.