Can nuclear fission or fusion occur together with bond formation in a reaction?
It has been done, not with bond formation but rather with bond breaking, and is called the Szilard–Chalmers reaction (credit to Loong for pointing out the name).

When a biphasic mixture of ethyl iodide (with stable $\ce{^{127}I}$) and water is irradiated with neutrons, all the radioactivity from $\ce{^{128}I}$ is found as iodide in the aqueous phase; there is none in the organic phase.  This is because $\ce{^{128}I}$ is initially formed in an excited state that emits a γ-photon, and the recoil from that is more than enough to break the C–I bond.

The energy of a γ-photon is > 10 keV; in comparison, the strength of a typical chemical bond is ~ 1 to 10 eV. The C–I bond strength is roughly 2.5 eV.