Sure could Lippy but t's a little bit of a different problem.Doug, on my house air conditioner, it would trip the breaker once in awhile, it's getting old like me I guess, anyway, they put a hard start kit on it, looked like a capacitor to me,...no more problem, could ya do that on an air comp motor?
See your drawing a little too much current so he wired up a cacitor in parallel on the line side of your motor. You have more than enough power (watts) to run your motor and everything else in your home. If you have a 200 amp service you have 48000 watts available.
Mike's generator only has 4400. He is just lacking enoug power to start the motor wile it's pump is under such a heavy load.
What your capacitor is ding is storing potential unill such time that it is demanded. Thereby decreasing the load drawn (current) from your panel.
Honestly, if your home is old, it may not be the a/c, could be the breaker. It's easy to check with a peak/hold clamp on meter.
Just my 2 cents.