It won't.

Read the chart I posted.................it's titled 5.56 / .223. HS dimensions are the same.

The only way it might make a very small difference is if the manufacturers are different & that would be very small.

But, per the chart, Military No-Go gauges (dimensions) are considerably larger, if his set happens to be Military by some enchanted stroke of luck.

You really should make an effort to find out exactly where you are on HS.

Use masking tape in layers, carefully trimmed to the HS gauge head & see how much more thickness it takes to not allow the bolt to turn, assuming you've removed the ejector & the extractor.

If it falls within the Military spec, that will give you some valuable info & it it does, then you can feel more or less OK with it, & then just keep the brass separate.

Maybe not ideal, but usable; otherwise, it's trash.

MM