Can atoms delocalize over multiple equally probably bonding structures in certain cases?
If it happens at all, it exceedingly rare. Through my 10-years work in chemistry, I didn't once found a case where it may be relevant. However, what does and indeed affect chemistry is reversible rearrangements.
The simplest case is rotation of molecules around single bonds. Another one is nitrogen inversion. More complex cases also exist. Such things sometimes make interpretation of NMR quite difficult. NMR gives a peak for each non-equal nucleus in the molecule. When internal rearrangement is involved, it sometimes makes two atoms 'equal', i.e. exchanging places too fast for NMR to catch the difference and producing a single peak instead. This, however, is 'quasi-delocalisation', since there is no need in resorting to delocalisation to explain said phenomena.
Another quantum phenomena often observed is tunneling. It affects slightly effective reaction rates/barriers and vibrational spectra.
Anyway, de Broglie wave length for proton is thousand times smaller than for electrons, so quantum effects in nucleus movement usually overshadowed by quantum effects in electrons movement.