If speed and only speed is the sole reason for owning a bike, or riding a bike, a road bike that is in the "racing bike" family will be slightly faster than your current bike. Very slightly.

I have a regular twenty mile circuit that I've ridden with a "pure" racing style bike, a touring style road bike, a mountain bike, a three speed beach cruiser, and a one speed beach cruiser.

Without a doubt, the "pure" racing bike is the fastest. But, the differences between my average times with that bike and a touring bike or mountain bike are trivial. And, the differences in average times between the mountain bike and the three speed beach cruiser are also surprisingly small. And, over a level twenty mile ride, the one speed beach cruiser is not much slower than the three speed beach cruiser.

Why are the differences in speed so small on different bikes? Air resistance is a minor factor when riding at around 15 mph, which is the typical speed range of someone riding alone in stop-and-go urban conditions. Air resistance becomes significant at about 20 mph, which is faster than most urban riders average when riding alone. And, air resistance is a HUGE factor at the 30 mph speed a Pro will average in a short time trial. But, YOU are not gonna average 30 mph through urban traffic even if you have a $5,000 Madone.

The real limited factor from someone riding alone (without other riders to working as wind-breakers) in stop-on-go urban riding is leg speed...the ability to stop at a red light, and then quickly resume a high cadence. And, building leg speed does not require a different bike, or a more expensive bike. It requires riding 300 or 350 days a year and constantly striving to build more leg speed.

Buy a road bike if you want one. Folks should own three or four bikes if they have storage space, and can afford them. But, don't assume the road bike will make you "faster". What will make you faster, if that is important to you, is learning to obtain, and maintain a high rate of cadence.