No, when you're downrange from a suppressed rifle you won't hear the rifle go off at all. What you'll hear is the supersonic crack of the bullet breaking the sound barrier, which sounds just like someone firing a 22LR high velocity round (or maybe even a 22 mag) right next to you. This crack is very loud, just like someone cracking a bullwhip. This will sound like it came from the closest point in the bullet's path to your ears/microphone. That's why there's hardly any delay between the sound and the hit. The suppressor conceals the location of the shooter by denying the advantage of hearing the muzzle blast. Almost everybody was looking in the direction of the target in this case.
IF that round was actually fired from an unsuppressed 30-06 from 200 yds away you MIGHT hear the report AFTER the bullet strikes but it would likely be unnoticeable due to the crack up close, the bullet striking flesh, and everybody losing their shit around you. IF the round came from an unsuppressed 30-06 up close, the BOOM of the muzzle blast would be super loud and the only thing you could hear. Everybody in the crowd would look in the direction of the shooter in either case.