You would improve speed, but possibly not by much. 1, 2, maybe 3mph. And although you would see a slight improvement, you (i.e. your legs, heart, and lungs) would be exactly the same. Any increase in speed will be a result of the lower rolling resistance via tire selection, and aerodynamics from the newly available lower body position in the drops of the road bike handlebars. Lowering the head even an inch or two, which can also be arranged from repositioning on your MTB, can result in a couple mph gain. Curious, what continental tires do you now have an how wide are they?