A guy like me riding a road bike can blow by another guy like me riding a mountain bike like I'm standing still.
What does this mean in terms of my commute time? Actually, not that much difference. 3 to 5 minutes maybe over 6 miles. In a race losing by 3 to 5 minutes more than likely means that you're are well back of the leaders. For commuting? It's up to you whether that amount of time is important.
A shorter commute with a lot of intersections or other places you need to slow down will make the difference between a road bike and a mountain bike less noticeable. A long commute on open roads will be more favorable to a road bike.
Your not going to turn a 60 minute commute into a 30 minute commute by switching to a road bike. I think you'd be lucky to shave 10 minutes off. That's not an insignificant amount of time, but it may not be what you were hoping for.