No. That's a completely different issue.
Single phase pool pumps are 'capacitor start' induction motors. They are a completely different animal to a DC motor. The capacitor is needed to simulate a rotating magnetic field in the stator, which induces a voltage into the rotor, which has no electrical connections to the outside world
Once it's running, the capacitor is automatically removed from the circuit. And the reason you use a 400V capacitor on a 240V device is because 240V is the RMS voltage. (Kind of like the 'average' of the sine wave) A 240V rms sine wave has a peak voltage of 340V. So that's why we use 400V capacitors.
(Looks like I'm putting my hand up as the resident electrician...)







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