I would and will try to grab a a full hand brake (not easy in a trad ) as well as a foot brake in an emergency as this is more likely to give you four wheel braking. Watch the rally boys they constantly use the handbrake to slow and control the car.
If the pedal doesn't give you four wheel braking then there's something wrong with the system. Using the handbrake in tandem with the hydraulic system in a Morgan won't force the shoes against the rear drums any harder.
