No matter how fast you get, you're not going to shorten the commute time much. Do the math: from 12 mph to even 24 mph you'd save only 10 minutes. But with sidewalks and any stops, you can't average 24 regardless so in reality the maximum improvement is less than that.

On my 7.8 miles the difference between as hard as I can go and loafing is around 6 or 7 minutes. I don't think that it's enough time saved to be a major concern (although I like to go faster for other reasons).

I know what you mean though - when I bought a bike for commuting it was a road bike because I didn't want the roadies naturally going faster than me. They were still faster, but it wasn't the bike.

Clipless and Gatorskins won't improve your speed. A road bike being lighter, more maneuverable and positioning you for more power and better aerodynamics is the right tool but we'll still have to turn the pedals as fast as the roadie if we want to keep up.