I experimented with switching my heat pump motor between grid power and generator without turning off the heat pump first, but that causes it to quit running, I think it quits on an overload and has to cool the internal thermal breaker and equalize the system pressures before it restarts. Same occurs with the refrigerator compressor motor. It just shuts off completely and takes several minutes to restart.
So what is electrically happening, is it the momentary loss of power or is it the sine waves getting out of sync with the motor? Is the motor still spinning or has it already basically stopped?
I would think this is the same idea as if the utility power momentarily shuts off and then immediately comes back. Even at out house this will sometimes happen. If damage were to occur, would it be the capacitors, the potential relay, the compressor windings, or nothing really?

 

It is protection for the compressor motor restarting against pressure. If power is interrupted while running, it takes a couple of minutes for the pressure to dissipate before the motor should be restarted. Waiting greatly reduces the re-starting in-rush current to the same level as it would be on a cold start.