All that happens is there is no gas impulse to push the bolt carrier back to clear the chamber and load the next round. The recoil may push the BCG back a little, but it will not be enough to extract+eject the spent casing and chamber the next one.
This happens when the gas system (aperture, gas block, and/or gas tube) gets clogged with deposits.
As a word of caution, intentionally doing this, and then loading hot rounds to try to make the recoil function the BCG will lead to dangerously high pressures in the chamber, and that equals a kaboom in a big way.
Thanks for the info. I'm not planning on doing this at all but I have to admit I have a soft spot for bolt action ARs (very common in England) and saw a high caliber bolt action Savage the other day that piqued my interest. Nevertheless maybe for my 2nd build - I'm going a much more "conventional" path for my first AR...