Two points, one against and one emphatically for yours:
Against: In 1999, the dot-com bubble was very close to fully inflated. Companies were desperate to lay hands on any tech talent they could grab, and it's possible that a 24 year old with reasonably good skills could be overemployed on a project like that. This is even more likely if the company in question didn't think they would have a Y2K problem.
"Hey boss - is anyone working the Y2K thing?"
"Uh no, I don't think so - none of our code is that old."
"Mind if I have a look anyway?"
"Knock yourself out."
For: I did know greybeards working actual Y2K issues. One particular drunk I knew pulled down $300K+ per year sifting old COBOL code between 1997 and 1999. I am fairly certain that extra cash allowed him to drink himself to death in style. He wasn't running any projects, but he was definitely deeply involved on the tech side. From talking to him during that time, he wasn't really turning up a lot of issues. Seems that even those old programmers weren't quite as lazy/resource-aware as they had been portrayed or, as above, a ton of that 2-digit code had already been replaced by more modern methods.
So yes, it's possible he led a Y2K-sniffing project in 1999 but in a company that ran nothing older than Java anywhere. How much that project actually mattered to anyone besides him is almost certainly being wildly inflated.