No, torque is the only thing that determines acceleration (along with mass of course). Acceleration = force/mass, where here the force is the toque at the wheels. If you build an engine that revs twice as high say, so produces loads of power but the same torque (like an F1 engine say), that allows you to use a lower gear ratio, so more torque gets to the wheels.
People say that power determines your top speed, what they really mean is that torque and gear ratio determines top speed.
Have a look at this for an explanation of torque, power, work etc.
Nothing to do with when to change gear really though, so sorry for the !