Not really. The handlebars aren't to prevent instinctive intervention, but rather to guard against accidentally bumping the controls during high acceleration. At that point the airplane is physically attached to the catapult; the autopilot isn't doing anything. As soon as the aircraft leaves the catapult the pilot takes the controls again.

There is no automation in takeoff for current USN carrier based aircraft. The F-18 is the most automated, and the process is this:

1. Pilot sets takeoff conditions (throttles, flaps)

2. Pilot signals deck crew

3. Catapult accelerates the plane off the deck

4. The plane's fly by wire control system pitches the plane for optimal Angle of Attack for the wings (IIRC - 8.1* without flaps).

Once the aggressive acceleration of the catapult is complete, the pilot takes control again and begins flying - this is less than 1 second after catapult release.

Here's an example catapult launch from a USN F-18 pilot: https://www.youtube.com/watch?v=Nj9D1Ls-_JM

If you look at the stick directly in between the pilot's legs, you'll see him put his right hand on it at ~4.5 seconds. His left hand is on the throttles.

No that's not how that works.

That is how Prof. Missy Cummings presented it in MIT's Human Factors class ~6 years ago. I've never seen a fighter cockpit, but she was a pilot herself, so I'll take her word for it :)

I've heard her tell this story. My impression (as I recall) was that it was to show the catapult operator that you weren't touching anything. But even though this is just about being flung mechanically off the deck, the basic idea applies. When the automated system is doing its thing, it can be harmful to interfere.