No, an APU is (in most aircraft that have them) actually a small jet engine that GENERATES electrical power, as opposed to storage. In some aircraft, the distinction between the onboard battery and the APU is quite clear. I know one jet that this is true of the the A320 family.

The startup procedure for that aircraft relies on either a tether from the ground to provide external electricity, or on the battery to provide electrical power to the instruments/HUD before the APU is spun up.