Suppressed ("silenced") rifles make very little noise at the barrel, but if the bullet is faster than the speed of sound, it still makes a noise (and according to this article, that is what is tracked).
Having a suppressor wouldn't help, unless terrorists were using subsonic ammunition. But subsonic rounds are really, really wimpy, and won't penetrate armor.
So the system would work very well against enemy snipers.
Then you will have a vastly less-effective sniper. Subsonic rounds are required for sound-suppressed fire and the benefit of a rifle is speeding a large bullet up to high (supersonic) velocitities that are capable of penetrating body armor, lightly armored vehicles, and maintaining a flat trajectory to a distant target.