Things will be a good bit simpler if you have it mounted on a wheel. Not all roadside assistance people would have tire mounting equipment available, particularly those that respond for cars, vans, light trucks, etc. Certainly if you need to change the tire without assistance, it will be a much less daunting task if it's mounted than if you have to unmount the bad tire and mount the good one yourself.
Most of the hoist thingies I've seen hoist the wheel, not the tire itself, though I'm sure there are plenty of variations around. I know mine uses a cross bar that fits through the central hub hole of the wheel.
One caveat: if you are unfortunate enough to have different types of wheels for the various positions, it probably is impractical to carry the spare mounted. I suspect you can use identical wheels all around (same offset etc.), though.