Does a bigger rear sprocket give more horsepower???

[Dead Eye]

Acceleration is a function of Power and Power is a function of Torque (Horsepower = Torque x RPM/5252)

Also, from the article above, "One horsepower is the power needed to move 550 pounds (249kg) one foot in one second."

If altering the gearing causes increased acceleration, that power has come from somewhere.

As I mentioned previously, you are moving the available power around by adjusting the Torque at the wheel (as Power is derived from Torque and RPM). So you may have increased / decreased peak available power but at the expense of other variables.

... I think... it's all interesting stuff - good mind exercise