Most APs are certified for use from 400' above-ground-level on departure and on a complex departure procedure or in weather, that's not an uncommon engagement level.

There's a fair number of people who think that pilots are relying on "George/Otto" too much and should do more hand flying, but I'd imagine if you peered into 100 airliners on departure, that 95 or more of them are on autopilot somewhere below 5000' AGL.