"Every hull has a maximum spee
"Every hull has a maximum speed that it can attain - at least as far a production boats are concerned.
Since the coast guard formula for maximum horsepower is also based on the measurements that are used to figure hull speed you can use a "rule of thumb" formula to fit the best overall horsepower to a given boat.
By installing a motor that is 80% of the max listing on the plate you get a couple of things.
Firstly, you get a motor that is neither too big or too small for your hull. A side effect of that is that you get the best all round "gas mileage" as well since you are neither over working a motor that is too small nor wasting horsepower which is unable to increase the speed beyond what the hull can realisitcally achieve.
If you are interested in the math to figure maximum speed for a production "planing" hull it's simply the square root of the hull length at the waterline, multiplied by 1.34 multiplied by 1.15 (the 1.15 part is to convert the answer which comes out as Knots into MPH) multiplied by 7 (7x the hull speed is the factor for a planing hull in most production boats).
So if you take a typical production hull in the 16 1/2 to 18 foot range which has a waterline length of 16 feet (just to keep the math simple enough to do in my head) you would calculate as follows:
square root of 16' = 4 x 1.34 x 1.15 = 6.16 mph x 7
So the hull speed of 6.14 mph (displacement speed) x 7 = 43 mph (43.148) which would be the max speed, regardless of horsepower for the ficticious hull I used.
Most aluminum fish/ski production boats in the 16-18ft class would normally be rated for about 125 horses max - so 80% of that would be 100 horses "optimal".
And just like magic, if you hang a 90 or 115 horse motor off the back of one of them, you will see top speeds in the low 40's.
If you hung a 350 horse off the back (assuming the transom didn't depart from the boat) you would still only see the low 40's before the hull became so unstable that you could not handle it.
When you see one of those racing boats "lose it" first lauching into the air and then do cartwheels across the water, it's because they have exceeded their maximum hull speed (which has been engineered to factor significantly greater than 7 found on most "off the shelf" boats).
Now that I have skirted your original question - as Jeff states it's yes/no. In general, all else being equal, you need more horses to turn a larger prop.
But it you have a "bigfoot", take the 60 horse for example, you can turn a bigger prop than the 75 horse (regular) model because the gear ratio is significantly lower on the bigfoot's.
It won't give you more speed in that application, but will give you more thrust to push along either a heavier boat or one that is more hydrodynamically "challenged" (such as a pontoon).
Fitting a motor and a prop are not rocket science projects, but I guess my point is that there is no "one size fits all" answer and each boat has to be considered on a case by case basis since numerous factors can be different even between two boats that are exactly the same..."