For 12 seasons, it was unclear about how Elliot and Kathy met. It was clear that they got together while still young as in high school sweethearts. It was also (quietly) known that Elliot and Kathy got married while expecting Maureen. It wasn't until Gray when Elliot was investigating a rape case at Hudson University involving with alcohol. John Munch reminded Elliot that he met Kathy over a keg at a frat party. However, Elliot was never a frat boy (he went into the Marines first then community college taking night courses while he was already married) and it was more romantic than the way John described it. Later, at home, Elliot was thinking about it and wondered what would've happened if they hadn't gotten drunk despite after being married for 26 years and 5 children. Kathy remembered how much she wanted to kiss Elliot, but she didn't because she was scared. Meanwhile, it took Elliot 3 beers to work up the nerve to say Hello. Then they both got really drunk. But Kathy wasn't drunk enough to know what she was doing
It very much sounded like they were attracted to each other, love at first sight, but needed alcohol to boost up their confidence. It's very possible that Maureen was conceived that night but it wasn't said. It's also very possible (and I'm believing it) that both Elliot and Kathy were both in high school students who snuck out to go to a high school or college party thrown by mutual acquintances. By 20 years old, Elliot was already married with a child and went into the Marines when he was 18- so estimating that both Elliot and Kathy were about 17 years old by the time they met and married. Back in season 1's Sophmore Jinx, Elliot grounded Maureen for sneaking out late at night and was in her room for days; if Kathy's parents grounded her like that then Elliot and Kathy wouldn't have had Maureen.
In Gray, Elliot was probably wondering if Kathy thought he took advantage, but not so as Kathy felt the same way. Plus he wanted to know why Kathy just didn't go up to kiss him- a complete stranger!