You could say it works (for it still threads) but I'm just not crazy about the half-missing threads.
As on some Reed vises, are there other Athol vises that share the same main screw/spindle? Surely, someone else has been down this road before...
Sadly, the days in which you could just order replacement parts from the factory are long gone.....by 40-odd years, or so........
However, if the threads in the main nut are still good, and you have a friend who does turning work, its not as bad a job as you might think to simply make a new main screw for your vise.
The Athol make uses a 'buttress' thread configuration, which is as easily done by single-point threading, as is any other thread-form. You (or your turner) can simply use an undamaged portion of the original screw as an improvised gage for the threading tool, and simply take pass after pass, til the new screw fits the nut freely.
One does need the rigidity of a 'medium heavy' lathe for this work, of the Hendey, Monarch, or Lodge&Shipley class. A 10" South Bend. or similar, needn't apply.
I've done a few vise screws this way, one time and another, in the more common square and Acme threads. It is a somewhat tedious job, to be sure.
It helps to have the bar stock in a heavy pattern 4-jaw, and initially turn only the threaded portion to diameter for the thread work, then bring the rest of the screw length to diameter after the threads are done, to maintain as much rigidity in the setup as might be.
(and, no, I'll not take the job, myself, I get to be 'retired' these days.....it should be easy enough to find someone here who does turning, if one asks nicely)
cheers
Carla