Sorry for not responding earlier; I had to think about this a bit. Whether the presence of astronomically large numbers can make you vulnerable to Pascal's Mugging seems to be a property of the interaction between the method you use to assign probabilities from evidence, and your utility function. Call the probability-assignment method P(X), which takes a statement X and returns a probability; and the utility function U(X), which assigns a utility to something (such as the decision to pay the mugger) based on the assumption that X is true.

P and U are vulnerable to Pascal's Mugging if and only if you can construct sets of evidence X(n), which differ only by a single number n, such that for any utility value u, there exists n such that P(X(n))U(X(n)) > u.

Now, I really don't know of any reason apart from Pascal's Mugging why utility function-predictor pairs should have this property. But being vulnerable to Pascal's Mugging is such a serious flaw, I'm tempted to say that it's just a necessary requirement for mental stability, so any utility function and predictor which don't guarantee this when they're combined should be considered incompatible.