I am not familiar with the doll in question. And I don't quite understand the question.Will the Titan bond allow her neck to still move?
However, the threaded rod you show is rigid (i.e. it does not bend). The titan bond, applied to the threaded rod and inside of the tube, merely 'fixes' the two ends of the break together. It will not allow any bending at the break (obviously). But the normal movement of the neck and head at their joints should be unaffected so long as the tube does not interfere with them.
You would probably only need about 1" to 2" of tube (the longer the better) to fit over the threaded rod. Apply the titan bond to the inside of the tube and on the threaded rod, slide the tube over the threaded rod so it is centralised at the break, and allow it to set.
The tube does not have to be metal, so long as it is robust enough to take whatever forces it is subjected to.
To illustrate: In the photo, imagine the bolt is the lower part at the break of your threaded rod and the wooden dowel is the top part at the break of your threaded rod and the plastic tube is the tube you put over the threaded rod at the break & hopefully you will understand the principle of what I am talking about to 'join' or 'fix' the break. It is rigid. Any movement will take place according to whatever joints are at the opposite ends of the threaded rod.