Right now, you are looking for a solution yourself. Down the line, you will be able to twelve step and help such a person or at least see him as a reminder of what alcohol does to us.
I would suggest that if it really bothers you and distract you to go to a different meeting.
Some AAs might disagree with me but I feel that as a newcomer, you are already raw enough and should not have to practice patience and tolerance in what should be a nurturing, learning environment.
And yes, people who are under the influence are welcome as long as they want to quit drinking. Most are not disruptive but some are. Tolerance for disruption varies from group to group and also depending on the secretary.