The Arduino has the standard firmata sketch uploaded to it, the python code is live, so it sends commands directly to the Arduino over the serial pins and is not saved on the Arduino once the connection has been terminated. So in short, yes.
I had the same challenge. My workaround is to first startup Arduino IDE, check what com port you find your board. Alternatively you can use the Windows device manager to check out the port number once you have connected your Arduino. The nagging thing is that Windows is changing com numbers after reconnecting you Arduino. Maybe there is a way to force a number to your com port, or auto detect?