If you ordered a true Nato HS Gage , yes .
The issue we have discussed here is, it depends on who made your barrel . As Mrraley points out in his Technical thread for Armalite HS , Armalite uses actual 7.62x51 Chamber spec's . a lot of the other Barrel manufacturers use hybrid Chambers for their marked 7.62x51 Barrels & unless you get their spec's for a HS Gage , no HS Gage will be perfectly correct for their Chambers. Its why I use a 308 HS Gage's for testing , because basically the 7.62x51 is a 308 chamber . Just look at the differences in the two & where they are different dimension wise .
Now if I was going check a AR 10's, HS , I would use a Nato 7.62x51 HS Gage set , because I know its what is used to finish the chamber.
Winchester introduced the .308 cartridge to the sporting world in 1952, and was adopted as the official U.S. Military cartridge in 1954, even though there were, at that time, no suitable military weapon adopted nor chambered for the round. The early military nomenclature was T-65, which was still technically an ‘experimental’ cartridge and rifle, having not yet been adopted.
When the trials finally came to a halt, the .308 Winchester was adopted into the U.S. Military as the 7.62x51mm, later accepted by NATO, and known as the 7.62x51mm NATO.
The external dimensions of the .308 Winchester and the 7.60x51 NATO cartridge are identical in every way, and completely interchangeable, the differences being the web of the military cartridge is thicker near the base, creating a lower internal capacity, thus necessitating a smaller powder charge to achieve identical ballistics, and a slightly larger chamber dimension, due to the nature of military use; dirt, dust, mud, and sand inevitably being ever-present on the battlefield.