Why would it? People always seem to assume that with extremely long lifetimes, humans would still reproduce at roughly the same age as they do now. I just don't believe that would be the case.

So many things change with lifetimes that long and it seems more likely to me that the human timeline would adjust to the new lifetime. Physically maturing into an adult may take the same amount of time, but now it's a tiny fraction of your overall life. You may spend 50 or 100 years in secondary education, then another 200 in a career at which point you should have enough money put away to live on the interest.

And it's at this point, when you're 300+ years old that you start having children. On this timescale, you'd still see more generational overlap than we have today, but no so much that overpopulation is a concern.