Not trying to be sarcastic...but what SPECIFICALLY does the Transfer Case Support Rod actually do?
SO LONG AS, you kept all your motor and trans mounts tight, Crossmember bolts tight, as well as your bell housing bolts, then you should be OK without the rod. However, I'll assure you, it serves a purpose that GM thought necessary or they would not have spend the money and time to install it. Think of the millions they'd have saved by not installing it on all the 4x4 trucks they built. BUT, then there's this. Could it have been used to keep the Tcase, Trans and Engine all stable as it traveled down the assembly line and once mounted in the truck it really was needed? There are some thing that do work like that. Not sure if this is one of those or not. But I like to think anything that people say, Ohhh you don't need that, yes you do or GM wouldn't have spend the money and time to engineer it, the cost to have it to have it made, the time to install it, etc if it was NOT necessary. While all that is true, it is also true some parts are for just assembly purposes and it's worth it for GM to have those parts just to make it down the assembly line and held in place until bolted into it's permanent home, and then yes, it wouldn't be necessary any longer.
Point being, if you have it use it, if you don't, I wouldn't lose sleep over it.