I know this is an old thread and as usually happens the OP has not followed thru with letting us know how he's done, but here is my input.

7/16x20 is really an odd size for any hole on a bow. For as long as I can remember (35+ years) most holes were standardized by the ATA. Most all threaded holes for stabilizers and cable rods were/are 5/16x24. Today there are no threaded rods being used. They are all 3/8" rods just pressed into a plain 3/8" hole and secured by either epoxy or a set screw coming in from the side of the riser.

Eders.com has a Cobra rod for $11 that is threaded that may work. If the hole in the riser is 5/16" I would drill it out to 3/8" and drill and tap a hole from the side for a set screw to secure it. In fact, I'd drill and tap for a set screw no matter what rod is used. Then just cut the threaded portion off with a hacksaw and bevel the end with a file. Buy a cable slide with the rod and no extra cable separator will be needed.

Parts for old bows are just about nonexistent so you have to think outside the box and be willing to improvise.

But to answer the original question? Yes, a cable rod/slide of some sort is necessary if you're getting any fletching contact at all, especially if shooting vanes.