A null hypothesis is a statement about parameters, while the virtual sample is a statement about statistics, so it's not quite correct to say that virtual example is the null. And the null isn't the same as the prior; the null hypothesis is, as the name implies, a hypothesis, while the prior is a confidence level assigned to a hypothesis. So, for instance, "I think the null has a 90% chance of being true" would be a prior.

Your last paragraph, thought, is correct. The correct test would be a Poisson distribution with lambda = 0, and the probability of getting a non-zero value when lambda = 0 is 0.