Well, as you suspected the answer is complex.

A road bike is lighter with lighter wheels so you can accelerate faster. A road bike is probably a little faster in the corners. And you are more aerodynamic on a road bike, so you probably have a higher max speed. Cruising say at 20+ mph is much easier on a road bike then with the more upright posture on a hybrid.

There are times when hybrids are faster. That would be for potholes, RR tracks, rough pavement, road kills, sand etc.

With an 18 mph avg you are probably cruising about 20 mph or even a tad bit faster. Aerodynamics starts to kick in at about 17 mph, so you would probably have a small but noticeable speed increase on a road bike from .5 mph to as much as 2 mph. Now you may go nuts with the "sporty feel" of the road bike and average even more, but then your power input is different and the effect as more motivational then anything else. And then again, if you hate the feel of a road bike, it might not help one little bit.

I had a friend who rode an old clunky sport touring bike for years. He had this one gear that he loved to ride in. Then he got a brand new road bike with ultegra and he went SLOWER. We figured that he lost his "magic" gear or something.