On this page it says
...if HA holds, the p-values have a distribution for which values near 0 are more likely than values near 1. However the p-values may have a distribution that is not rectangular if H0 holds. The more general result for a test with a composite null hypothesis is that p-values are no more likely to be near 0 than to be near 1 when H0 holds -- the distribution may favour values near 1.
Should I take this to mean that if I simulate or maybe bootstrap a distribution of p-values, I can make some kind of informal inference about H0 based on the skew of that distribution? If so, where can I read more about this technique? If not, why not?