No. And here's why:
When the plane is trimmed out very little pressure is needed to fly the plane normally. And remember, there is a limit to what torque the servos can output and other software parameters that will make it auto-disconnect for safety.
When clamped even with just a few inch lbs. of torque, The clamp refused to move. And I tried to move it, believe me!
So, when it was time for the final install, I torqued it down even more till the bracket tabs just barely started to deflect. Sorry, I cannot recall the exact final torque.
I did toy around with bonding and/or drilling a small, matched hole and have a mechanical bond, but in the end, I decided that simple is better and left it alone.
I did place a witness mark on the tube so if it did move, I would see it. (a separate checkoff block on the annual inspection.) It's been checked once @ 125 hours. No movement.
To be fair the autopilot was used just for set up and maybe a few times more the first year. I'm using it more now, so this Aug. we shall see if it moved.
Plus - if I ever had to remove the push/pull tube it would make it somewhat easier.
If it makes you sleep better at night, by all means do what you think is necessary to secure the clamp.
All the best!