Secondly, most people who get drunk during the flight actually get drunk by drinking too much during the flight, with very few people actually reaching the airport drunk. Also, airlines have got far more strict in terms of what they allow and what they do not, so if somebody is already drunk when boarding, an airline may actually restrict the person from boarding. But very few people take a trip like this person did (link to article):
A drunk Norwegian tourist raised a security alarm at Rome's Fiumicino airport after he fell asleep on a baggage belt and travelled 160 feet before being spotted by an X-ray scanner. The 36-year-old arrived at the international terminal of Italy's busiest airport at the end of last month with a backpack and a can of beer in his hand. The Norwegian was due to check in for a flight to Oslo and when he found no one on duty at the airline desk he leapt across the counter and fell into a deep asleep on the baggage belt with his bag beside him, the Daily Mail reported.