Hmm. You've asked a classical question about a quantum-mechanical system, which makes it a bit hard to answer precisely. But the answer to the spirit of your question is "yes".

It's more precise not to think about subatomic particles in bound systems as "meandering" so much as having non-zero probability of being found in different places. And the probability of any scattering interaction, including nuclear decay, will depend (amongst other things) on the overlap of the initial and final state wave functions. So yes, it matters where the particles "meander."

A great example of this is K-capture, or inverse beta decay. This only happens almost entirely with S-shell electrons, since P and higher angular-momentum electron wave functions go to zero at the origin. Only an S electron "spends enough time near the nucleus" to be captured with any significant probability.