For instance, it seems like time has a smallest divisible unit, Planck time.

We don't really understand what the significance of the Planck time interval is. In particular, it would be extremely surprising, given modern physics, if it were a discrete unit like the clock cycles of a computer or the steps in Conway's game of life. It could be 'indivisible' in some sense, but we don't know what sense that could be.

Then to try answering the question, if you describe a series of events which can only happen in 1 particular branch of the many worlds interpretation, and you describe something which happens in 0 branches of the many worlds interpretation, then my understanding is there is no series of events which has a probability in between those two things, which would appear to imply the concept of a smallest unit of probability is coherent and the answer is "Yes."

Branches of the wavefunction aren't really discrete countable things; they're much closer to the idea of clusters of locally high density. Relatedly, even when they are approximately countable, they can come in different sizes.

Many worlds is in some ways a really bad way to understand probability. Probabilities should be based on the information available to you and should describe how justified hypotheses are given the evidence. The different possibilities don't have to be 'out there' like they are in MWI, they just have to have not been ruled out by the available evidence.