Yes, you could. You would, in effect, be moving the trim function to the pot that you added, BUT... You may have created a situation where yout trim tab on the xmitr is back to center, but that is only cosmetic! You are still biasing the joystick pot's output to compensate for mechanical or electrical defect. When you apply that bais, you lose effective range of the joystick throw (you can add so much bias (or 'trim') that you won't get any response from the joystick in that axis).

You would also be unbalancing the that axis of the joystick. I don't think that the trims are in series, I think they are in parallel to add or subtract (add pos or add neg) bias voltage. You would just be contributing to the problems.

Better to determine the reason that the h-bridge on the driver circuit is not zeroed when the joystick on the xmitr is centered.
If it is really that big a deal to you, or if you lose function in that axis, my first suggestion is to try another driver board, or find a hameture radio guy who is willing to trouble-shoot the driver board and xmitr and maybe fix it.

more likely, just live with it.

Splat