The answer is yes, but as hes been explained above, it's more complicated than move the gear ratio one way to raise speed, move it the other way to raise acceleration. You can tighten your gears and decrease acceleration, and vice versa, but generally that doesn't happen.
For a given speed your acceleration is determined by horsepower. The gearbox's job is to keep the engine spinning at the RPM for best power (in the case of a race car). Some cars are very peaky, and only produce the top 25% (random number I'm using for example) of peak power between a narrow RPM band. This car is going to want very close gearing, and if it was geared for top speed, the acceleration would probably be slow. On the other hand some cars have relatively flat power curves and almost don't care how they are geared. With cars like that, close gearing can cause problems because of the break in acceleration that occurs when you change gears.