You'll know because -
1. The feed ramps on your barrel extension won't be lined up. Your BCG likely won't go into battery.
2. Your gas tube will be tweaked/bent/crimped. Some people have spun their barrel 1/2 revolution or more before realizing what happened.
3. Or, worst case scenario, the index pin won't shear but (because of improper torquing from the factory) your barrel will turn in your barrel extension; resulting in replacement or very costly repairs compared to a sheared index pin. And yes, this scenario has happened to members here. Improper procedure in the meloniting process can significantly decrease the torque spec on the barrel extension.
Bottom line, your best bet is to clamp the barrel when installing a muzzle device. Yes, 99% of the time everything will be OK, but it only takes once to make for a poopy day.
In theory, it should never happen; but obviously that is not the case. A couple of chunks of 2X4 and a bench vise is cheap insurance.