It wouldn’t have mattered if Einstein hadn’t discovered E=mc2. We’d still have had the A-bomb and other developments in quantum theory. And roughly in the same time too.
Otto Frisch and Lise Meitner
used MEE to understand the quantitative energetics of the experiment carried out by Otto Hahn which showed that collision of a neutron with a Uranium nucleaus produced the element Barium as one of its by-products. So, yes, MEE played a pivotal role which this relationship played in making the fundamental leap to the initial hypothesis that large atoms could split into approximately equal halves.
But would there be an MEE without Einstein? Yes.
Einstein
derived the formula from previously-understood laws of physics. The derivation involved
using the postulates of Special Relativity. In this method, the first step is deriving the Lorenz transformation, i.e., how space and time coordinates transform when the frame of reference is changed.
Early approximations of the transformation were
published by Voigt (1887) and Lorentz (1895). They were completed by Larmor (1897, 1900) and Lorentz (1899, 1904) and were brought into their modern form by Poincaré (1905), who gave the transformation the name of Lorentz, and Einstein.
Einstein derived the equation in 1905. Already, Max Planck had hit upon the Planck’s Constant. Even earlier, in 1896, Henri Becquerel had discovered radioactivity, and the next year, J.J. Thompson had proposed the plum-pudding model. In 1907, just two years after Einstein derived the equation, Ernest Rutherford experimentally deduced the existence of a positively-charged nucleus at the center of an atom.
Therefore, the basic principles behind E =mc2 had been around for a long time. Einstein’s genius was putting together the disparate strands developed by Poincaré and others. If Einstein weren't around, Poincaré would have had the best chance of discovering it, maybe not in 1905 itself, but certainly a few years later. Meanwhile experiments would have continued to produce the same results. In the end, it would have evened out, and we’d still have had fission.
Kaushik