When you throw a ball the work you do to accelerate it equals the kinetic energy the ball gains?

In short yes. However, lets say you lift a ball of the ground. and release it. you do not accelerate it by any means however it has kinetic energy as it is clearly moving. what happened there is the distance from the ground is potential energy once you release it it becomes kinetic energy.

when you throw a ball you use the potential stored energy in your muscles and convert it to kinetix energy as you move your hand. at the release the ball has gained nearly all that energy. some is lost in heat and friction.