Some friends of ours run a ProET class Dodge Challenger. It runs about 850hp on a mix of AvGas and pump fuel and covers quarters in 9.5 at 145mph - and does 130 foot wheelies. It's geared to about 155mph. They were approached by someone selling a supercharger that would make the engine good for near-on 2,000hp.
In present form over a mile drag race, she'd hit the quarter in 9.5 at 145mph and take roughly another 18s to cover the remaining three quarters, crossing the finishing line at 155mph. In supercharged form she'd hit the quarter in 7ish at 155mph and take roughly another 17s to cover the remaining three quarters, crossing the finishing line at 155mph.
Without the gearing to accommodate the power, the car would see no improvement in top speed at all - an identical Vmax - despite more than doubling the power. What it would see is an improvement in acceleration. The average course speed would improve, but then that's a function of acceleration as you know.
All power does is provide effort to overcome air resistance to give you more potential speed. I have a nice formula to calculate it if you want it. You need the gearing to turn the potential into a reality.