I'm no expert, but somewhere on the heat pump there should be a plate that tells you the minimum breaker size the unit requires. This is usually expressed in amps. Multiply the amps by 220 and you'll probably get a pretty good estimate on the watts needed for the start-up surge. The breaker has to be large enough to accomodate this without tripping.

As a rough instant-answer, I'd say you'll have problems if the genny you're talking about is a newer, small-diameter, 3600 rpm cheapy.  There just isn't enough rotational-inertia in those to do a good job of starting induction-motors.

On the other hand, older 1800 rpm large-diameter cast-iron gennys carry enough inertia to spin up an induction motor almost as large as the genny.  Assuming you have a good high-torque engine driving it....like a diesel.

I routinely start a 10hp 3-ph motor with a 12kva diesel genset; and the motor is driving an 8' x 3' rock shaker-screen deck...i.e. a massive startup load...