A non-auto transformer can take all of the 240V power and convert it to 120V on a single leg.
The way this works is that all the 240V goes into magnetizing the transformer core. At that point the 240V source doesn't care about anything going on with the transformer's secondaries.
At the transformer secondary there is the amount of power available that's been injected by the primary.
You can pull that power out via one winding, two windings, or a dozen as long as you don't pull more than was injected. If you do then all the voltages of the secondary taps will drop.
Furthermore, you must be mindful of the actual secondary wire size. If you exceed the rated current out of one of those secondary taps you will damage the insulation. If you want to feed 240 and 120V loads in a mixed and convenient way you'd want to size the transformer so that either of the 120V windings can output the full power being injected into the primary.
