Can a person have a stent procedure for his carotid and leave the hospital the same day?

Sometimes: Most centers will want to observe overnight to monitor for the occurrence of perhaps the most dangerous risk-that of a stroke. Should that occur, rapid treatment is necessary to prevent progression, in fact, very early recognition is necessary. Someone may be allowed to leave under perfect conditions, which may include proximity and an experienced, committed caregiver.

Yes but not standard: Yes, but it is not standard practice as it may be possible for one's blood pressure to either be too high or too low after carotid stenting. It is standard practice to monitor patients overnight. There is a baroreceptor at the location of the carotid stent which is thought to play a role in the occasional unpredictable blood pressure changes post-stenting.