No. They provide phase shift to give the single-phase induction motors a rotating rather than oscillating magnetic field. They charge and discharge 100/120 times per second depending on grid frequency.
They do not cover inrush current, and would need to be orders of magnitude bigger and a different topology to do so.
Still increases air resistance. It gets hit by air, and that pushes it back into the fuselage.
Larger aircraft commonly have a ram air turbine (RAT) or Air Driven Generator (ADG) to provide some electrical power and hydraulics in certain emergency situations.
On CRJs, it’s right up the front: https://www.youtube.com/watch?v=MxgPrpjByTE
Still delivers a percent or two penalty to fuel burn, and the tiny little generator doesn’t even come remotely close to making up for that.