Actually YES but it's not the way you mean. It's not that if you have your period at 11 your eggs are going to be 3 years older than someone who got it at 14. But there does seem to be some connection between unusually early and unusually late menarche and less than optimal fertility. In English - if you get your period weirdly young or weirdly old, a lot of times you're less fertile than people who got it at the average age of 12-14. There also may be a connection between more boys and more girls being born depending on if you had menarche at the average age (more sons) or on the extremes (more daughters). With tons of exceptions as the posters above demonstrate.
The studies are out there but for some reason I can't find them in a quick Google search and have to abandon the attempt. The studies are done by the same group of Japanese researchers that do a lot of the more interesting gender ratio studies.
Apropos of nothing, this popped up when I was searching and I thought it was kind of weird Welcome to Menarche Parties R'Us! I would have DIED if my mom threw me a period party. DIED.
