You are proposing to partition the data into two observations, namely "number of trials that were performed" and "the results of those trials".

The information you have after observing the first part and not the second, does depend on the researcher's stopping criterion. And the amount of information you gain from the second observation also so depends (since some of it was already known from the first observation in one case and not in the other). But your state of information after both observations does not depend on the stopping criterion.

Also, the most likely outcome of your proposed experiment is not .7n cures for some n. Rather, it's that Researcher B never stops.