On hard start kits and reduction of in-rush current for Air Conditioners
Part 4 shows that the addition of a Hard Start Capacitor and relay will reduce the TIME to start an AC, but not the peak in-rush current. It may be enough to help a generator start the AC, but it does not eliminate the peak in-rush. Only a Soft-Starter will do this.
https://hvacrschool.com/start-capacitor-inrush-facts-and-myths-part-1/
https://hvacrschool.com/start-capacitor-and-inrush-facts-myths-part-2/
https://hvacrschool.com/start-capacitor-and-inrush-facts-myths-part-3/
https://hvacrschool.com/start-capacitor-inrush-facts-myths-part-4/