To answer this question, we must know something of the final state of the atoms, that is, the state of the singularity inside a black hole. The singularity is something predicted by the classical theory of General Relativity. Nuclear decay, on the other hand, is a quantum effect, and as I'm sure you know, there is great difficulty in reconciling these two theories.
So the most cautious answer is probably "we don't know". I will offer some further insight though. Since most people think that strange things start to happen when matter is compressed down to the planck scale, this would tend to suggest that the singularity is really not an infinitely dense point but rather an object with finite (albeit ridiculously high!) density. In this case, infalling matter would likely be crushed to these enormous densities. Whatever kind of quark soup is created when matter is at such high densities is quite an unknown. It would seem to me that this new form of matter may follow different quantum rules, and thus it may not necessarily abide by normal nuclear decay.
Observationally, it is a moot point since any interactions that happen inside the event horizon will forever be unknown to the outside world. Certainly nuclear decay can happen as the atoms fall past the event horizon and towards the classical singularity, but this information cannot be transmitted to outside observers.