Is it OK to pull Category (Cat5e, Cat6 a, Cat 6a) internet cable around a corner constructed of threaded rod/ All-Thread?
This is a bad idea right off the bat because the threads on threaded rod are usually pretty sharp and could very well damage the cable.  

Pulling around a fixed object rather than a pully or sheave that rotates is never a good idea.  

The TIA/EIA standards specify bend radii, and sharp bends violate telecom standards, manufacturer's recommendations, etc., but usually does not violate the NEC which is what the inspector enforces.  In most cases the inspector and the NEC don't care if you compromise the performance of your cable as long as you don't create a safety hazard. The other standards may be good practices, and may be contractual obligations, but they are not the inspector's concern.