I've never seen a carotid artery pop. You have to be a really poor clinician to allow a carotid artery to pop. The very first signs of a carotid artery leak are altered mental status and neurological changes due to reduced cerebral perfusion. If the swelling is bad, the hematoma can compress nerves that result in voice quality changes or tracheal shifts. Generally, it's fatal.

Two people died last year because their carotid arteries popped two days after tonsil removal. They got an infection in the surrounding tissue which weakened the artery, eventually it started to leak until it all went boom in their sleep.  
One died before the ambulance arrived, the other died in the hospital. I've heard of many similar incidents. 

Also neck trauma can easily damage that blood vessel.