Answer
No.
Work Step by Step
As stated in the footnote on page 640, U-235 decays faster than U-238 (an Internet search shows that its half-life is about 704 million years compared to U-238's half-life of 4.5 billion years).
If Earth were older, uranium deposits would contain an even smaller percentage of U-235 than they do now. Fermi would still have needed to enrich his uranium fuel to make it go critical.