They can repair it and create temporary passageways at least. They certainly didn't create it but there is no reason to assume their mastery under the Empire was anything but complete and even post-Fall they maintain a better grasp of it than anyone else. It is also worth remembering the webway defends itself, it seals itself against the Necron Dolmen Gates, for example.
The fact is the Emperor had no chance of exploiting the network to the extent he hoped, even putting aside the fragility of the Terra entrypoint.