Almost certainly this is not the case, except maybe in extreme circumstances. My car, for instance, gets approximately 25 miles per gallon average, traveling at highway speeds of 80ish MPH average. If I drop to 70 MPH, I can get 30 miles per gallon.
This is because the ultimate factors in gas mileage are fairly simple. Your engine RPM will increase fuel, and the higher your speed, the higher your RPM is required to be to put you at that speed. The amount of RPM increase needed to put you at a higher speed is more than the rate of engine time running. In other words, increasing horsepower requirements is more costly than engine runtime requirements. You can leave an engine idling for an hour and use less than a trip a few miles down which may take only minutes.
That said, while going slower saves gas, the biggest part will be the acceleration/deceleration parts of it. Accelerating takes much more power in a short amount of time to get your speed up, so the faster your acceleration, the more your RPMs will spike, and the more your fuel consumption is. Deceleration too. Letting your engine coast, or leaving it in gear while not accelerating, means your engine is using little to no fuel and yet is still rolling forward. The more you can take advantage of this, the less fuel used.
In the case of high acceleration and harsh braking, you turn a lot of energy into motion, and then convert that energy to heat for the brakes. If you turn a little energy into just enough motion to get you there eventually, and then let the engine slow down until it almost stops as you arrive, you waste the least energy. Ideal real world is somewhere in the middle.