First off, it is much more the motor than the bike that makes speed. Of course all things being equal a road bike is faster than a MTB based commute bike, but there is a blurry area in the middle.
That said, my commute bike is an old 1980s Specialized Stumpjumper I got at a yard sale for 20 bucks. Of course I proceeded to put a bunch of money and time into it, and I do store it inside at work, but it is still ugly. The single largest improvement in speed (besides me loosing 80 pounds over the last 4 years or so) was going to 26x1.5 slicks that can be pumped to 100psi. My commute is around 5 miles one way, with an 800 foot climb. I can take 5 minutes off my commute up on my road bike easily, but, on our crappy roads in commute traffic I feel much safer on the dedicated commute bike (plus I'm not wearing out one of my treasured road bikes just getting to work).
Yard sale and/or Craigslist are great places to pick up a good starting point for a commute bike.