It's a sitcom convention, and it's fun to make easy brain-dead wisecracks about the guy who got married three times, but I think in real life most people who knew somebody like this would probably agree that only the first one counted. Neither of the other two were ever consummated after the actual ceremony, and in the case of Emily, he's got a pretty substantial case for abandonment. He did not marry Rachel in his right mind, and no court on earth would actually refuse to grant that annulment. There is no chance that, amidst the yammering about drug use and homosexuality, the fact that they were drunk would not come up.
Ross does not have three failed marriages. He has one failed marriage, an abortive wedding ceremony and a very strange date with Rachel. If Emily had actually come to the US and attempted to live with Ross, and THEN flew off the handle because Rachel was impossible to avoid, that would have been a marriage. As big a whiner as Ross is, and given his WE WERE ON A BREAK mantra, it really seems to me that he should be clinging to the points of law that work in his favor and make his slate cleaner. It could even have been a comic point, arguing about which marriages count and which don't.