With the battery removed, and the key OFF should my multi meter show any degree of continuity between the positive and negative battery cables?
No. Otherwise your battery would go dead when connected.
If you have radio with a memory or an alternator it will.
Or if the generator cutout is closed or the lights are on.
There will be some resistance read if there are any bulbs in the vehicle.
If it is a Model T and the key and light switch are OFF, there should be no place for continuity between the two battery cable ends.
Digital or analogue multimeter?
Ifn it's a digital meter, join the probes together and see what you read.
Ifn it's an analogue meter, connect the probes together and zero the meter first.
If the car is equipped with a diode cutout or VR then you may see some continuity between the cables depending on which way you connect them and which way the battery is installed in your test meter when it is set to resistance scale. Also if the light switch is in the dim or brite position then you will have continuity through the switch and bulbs if the car has light bulbs installed. If you have your foot on the brake pedal and your car has a stop light then you will have continuity. Unlike modern cars the ignition switch on your T turns off the IGNITION only. Lights, brake light switch, cutout, VR...all of these have a path to load the battery that is independent of the ignition switch. Of course accessory items also have a path through their control switching arrangements such as turn signals...etc.