The climb is an especially difficult case because the power input to the rotor is high, and the trimmed collective position is high, so the initial rotor decay is very fast. This makes the minimum rotor droop lower than in a level flight case, if everything else was equal. Combined is the fact that the climb inflow is farther away from autorotative flow means that there will be much more delay before the autorotative flow can drive the rotor.
Offsetting these negative effests is the fact that the tests performed for certification include auto entry in virtually all critical flight conditions, including climb. The FAA inserts a delay to simulate the reaction of an average pilot, and the climb is a maneuver state where the hand is actively trimming the power, so the delay in pilot reaction in a climb is very much less than a leisurely cruise. The FAA allows 1.3 seconds in cruise before down collective, but only .3 second for maneuver states such as the climb. This means that the auto entry is permitted to occur more quickly in tests (as it would be in reality). The net result is that auto entry from the climb should be not much worse than cruise.