IIRC, since the breakers were installed about 35 years ago, (goodbye fuses) we have never had one pop open.
And we do get a LOT of over-voltage.
IMHO, the inverter type mini-split power supply will not load down the 230ac line,
and try to pull in big surges of amps during voltage sags.
Motor power usage is controlled by two things.
A. Pulse frequency from the controller board. (Which has no power or RPM feed-back).
B. The voltage of the 230 AC line. (Connected to diodes to make DC).
In the case of (A), the controller has to get feed-back from the temperature
sensors in the system and/or orders from the remote control unit (via my thumb).
All of these inputs are way too slow to cause anything but a 'normal' change in current.
(B), A sudden drop in line voltage going to be buffered by
the charged capacitors in the DC power supply of the unit.
Any change in current draw will come after a time lag..
And, that change won't occur in microseconds, it will be slow and will be synchronous with the sine wave of 60hz AC supply.
Plus, I care a lot more about a mini-split
not getting zapped,
than anything else we leave connected to the grid.