Well... I'm really just endorsing what others have said here...

Yes, a road bike is made for going fast on roads... just look at most club racers as well as all (to my knowledge) semi-pro and pro riders - they do not race on hybrids.

However, yes... you can go faster on a hybrid or on a mountain bike and the biggest, quickest and cheapest change you can make to your current bike is to put skinny road tyres/slicks on.

If you are not riding with others, you could also look at getting aero bars on your bike.

At our club we do have riders in the lower grades that race on hybrids or on mountain bikes. But ultimately as people want to go faster they move to road bikes... they are lighter, more responsive and more aerodynamic...

It depends on how fast you want to go and where/whom you ride with... and these goals will likely change as you ride more... just adapt your goals to what you are enjoying and thinking you might try.

I can't answer any questions about costs, sorry... wrong country to advise you... but it should not be huge and def worth it