Every shoe on the market is super stiff now. Probably not. Do you get hot spots where the cleats attach on long rides? Do your feet arch down as the whole sole flexes?
The benefit of the road pedal will be weight, larger cleat (so they can make it lighter and stiffer), and the road cleat (not speedplay) has a flat backing so it feels nicer when you're jumping on the power. It will not make you faster.