You can never falsify statistical claims, tossing the coin infinitely often does not help, either. So the answer is no, these claims are not falsifiable.
But what you can do and what people routinely do is to falsify statistical claim with a certain precise probability, that is where "confidence intervals" come into the picture of statistical tests.
As far as immortality is concerned, you can say with appropriate high confidence that no human can live longer than 150 years which implies mortality with at least equal high confidence.
But I would say that the confidence of mortality is higher than that, since our experience with other complex systems that are instable increases our confidence.