CTC does not Support Right-Click functionality of Drills
Using a CTC and placing drills on the Custom Turret (Rotor -> Hinge -> Drill), you can use the drill while moving the Rotor and Hinge with your mouse, but you can't use the right-click functionality of the drill (which clears vastly more space without collecting any resources).
Putting the Cockpit and the CTC on the same Subgrid that the Drill is on or turning of "Target lock" on the CTC doen't change anything, the right-click functionality was not restored.
Also, placing the Block-Tool "Drill" in then Cockpit-Toolbar doesn't change anything regarding that, as it is greyed out while controlling the CTC.
As some kind of not really usefull workaround,. you can leave control of the CTC, then right-click for the drills, then control the CTC again to move again in order to clear out a bigger chunk with the drills. But that is not really a solution and more of a crutch if anything.
Attachment: The Setup that I used. Moving the Rotor and Hinge with the mouse while controlling the CTC from the Cockpit works fine and left-clicking to drill works as well, but no right-click functionality.