It might make things worse. If the mirror is visible from the front of the car, it's part of the frontal area. Blocking the flow off the windshield might change the angle of the oncoming air, but that would drive the drag toward similar to the stagnation point.
spacemanspif mentioned old Beetles. This is cribbed from racing 911s:
http://www.gerrelt.nl/section-aerodynamics/aerodynamics-vitaloni-mirror.html
Mirrors are problematic because the optical requirement demands a flat plate and they are located in a complex flow. Peep mirrors and fendertop mounted mirrors address this. Peep mirrors are closer to the drivers eye and can be smaller.
The Eolab is interesting. I wonder how much of that is not just styling. Ferrari took the opposite approach...once.
