The KA-50 and -52 destroy their rotors when the ejection seat fires, as shown in this simulation. That’s why the helicopter drops like a rock after the ejection seat fires - the blades can’t autorotate if they’re not attached.
Assuming the blades are still attached, the helicopter will autorotate down even if it is completely unpowered. It might lose some altitude initially, but like you said once the air is moving over the blades fast enough for them to spin they will do what they were designed to do.
One thing helicopters and planes have in common is that if they fail too close to the ground autorotation/gliding won’t help. Helis are generally more dangerous than planes for a lot of reasons, the biggest one being that they spend more time in the most dangerous phase of flight - landing.