No. The event being bimodal only implies that the probability is centered around two values, not that p =1 or p = 0 for those values. For example, take a biased coin that turns up head once in a million. This is bimodal with p(head) = 10^-6.

PG's argument appears to be that the error in your estimate of p is almost always larger than the value of p and one should invest as long as 2*p is also within the estimation error.