It depends on how much the person had to drink, and how long ago they drank. Alcohol is eliminated at the constant rate of about .015% BAC per hour, which is about one drink an hour. If a person had only one drink, the maximum intoxication they might have would be about .02%. Within one hour, their alcohol level would be about zero.
On the other hand, if a person had an alcohol level of .20%, twice the legal limit for drunk driving in most states, it would take over 13 hours for their alcohol level to reach zero after they stopped drinking. Any breath test during this 13 hour period would detect the presence of alcohol. However, after approximately 13 hours, when the alcohol was totally eliminated from the body, an alcohol test would give a negative result of .000. A person who has no alcohol in their system is not intoxicated, and a breath alcohol test of that person will give a negative result.
Sometimes people have the mistaken impression that alcohol stays in the system for a long time, as marijuana does. In fact, in comparison to most drugs of abuse, alcohol is eliminated very quickly from the body.