This is a somewhat philosophical question. Given that even after person A's death, there's a non-zero chance that a brain fluctuates into existence with exactly the same structure and memories as A's brain, does that imply that A is immortal as given enough time, even if for each fluctuation, it survives for only a short while, A's brain will fluctuate into existence arbitrarily many times and this will enable A to "exist" for an arbitrarily long time.
Your question engages many of the same philosophical issues as those raised by so-called quantum immortality (http://en.wikipedia.org/wiki/Quantum_suicide_and_immortality). Discussions of quantum immortality are generally centered around the many worlds interpretation of quantum mechanics. The introduction of Boltzmann brain fluctuations into the discussion is an interesting variation. In any case, this is a question that lends itself more to the tools employed by philosophers than those employed by physicists (although this doesn't stop some physicists from devoting attention to it).