The effects of adding neutrons to an atom
Even if such a phenomenon were to occur, and the resulting nuclei were sufficiently stable to participate in chemistry (they would not be sufficiently stable, in reality), the "inflation" of the charge of the nucleus would almost certainly have a negligible effect on the chemistry.  The nucleus is really really really tiny with respect to the length scales of bonds and the electron cloud.

To give an idea of the scales involved: the largest stable element, uranium, has a nuclear radius of about fifteen femtometers $\left(15~\mathrm{fm}\right)$, per Wikipedia, or $1.5\times 10^{-14}~\mathrm m$.  Bonds and electron clouds are measured in Angstroms $\left(10^{-10}~\mathrm m\right)$.  Thus, the nuclear radius would have to expand by well over $\sim\!\!100$-fold in order for the assumption of a point-charge nucleus to begin to fail.



It is well accepted that the effect of isotopic substitutions on chemistry primarily is due to the change in mass of the nucleus, leading to the kinetic isotope effect.  Another potential isotope effect on reactivity involves the change in nuclear spin, leading to a "magnetic isotope effect" only relevant for certain classes of reactions between species with unpaired electrons (e.g., organic radicals and/or various inorganic species).

Isotopic substitution does affect the behavior of nuclei in certain spectroscopies, however, leading to isotopic shifts.  The isotopic mass change can have noticeable effects on the vibrational spectrum, due to the effect on the local distribution of mass. As described in the link to ADF's documentation provided by Aesin in a comment to the question, these effects can also be seen in the hyperfine structure of atomic spectra.  As well, the NMR isotopic shift of light elements, especially hydrogen, can sometimes be observed.