Yes the Construction Tower needs to be in the same logistical network to be able to work. Is there a reason why you can't use a normal Roboport to connect it to the logistical network? Do you have a separate network for construction and logistic or is it one giant network?
The Idea of the Construction Tower and the Drone Recharge Station is to have small logistical networks. So that you are able to separate the network easier. If I would add an extender this wouldn't fit to the original Idea.
Of course I can add also a Logistical Tower. The downside of that would be that your drones would have a long way to recharge and that stations would be always busy.
If you want I can also add settings to change the radius for the logistical network.