High voltage discharge? I don't think so. I am not trying to say I know more than you, but I read in both a manual and online, plus heard from an ac repair tech, that capacitors are used for kick starting compressors. They are used to keep them from over working them selves and burning up faster.
This is indeed correct. The capacitor on a motor is to cause a phase shift. Single phase power on an electromagnet can only produce a push pull force. With a round rotor, this creates no rotary torque in a motor. A phase shift must be introduced by either a shaded pole (common in small low starting torque motors) or and electrical phase shift is introduced with a start cap with the start winding for a much higher starting torque.
A smaller lower current run cap is often used for motors such as fans that is used for both starting and running.
When using 3 phase power, the 3 windings provide the required rotary torque so no starting cap is required.
The cap is not for a capacitive discharge kick.
There is a great Wikipedia article on the subject for those who wish to increase their knowledge of the subject.