It's a space station, he knows that Cardassian and Klingon and Ferengi and all manner of other races are not drinking Synthehol. Jake and Nog would have no trouble getting the real thing, it just wouldn't be Chateau Picard.
I think synthehol works like nitrous oxide. It intoxicates you but only as long as you're still drinking it, the wear off effect starts within a minute or so of not ingesting it any more and is rapid, oxygen breaks it down. So you can have your hilarious drunken conversation at the bar but when red alert sounds you're clear headed within a few feet of running out the door.