Not any dangers that I know of, if you are starting a new pack. Starting in the middle may not offer proper protection, I can't say for sure, and it would depend on what kind of pill it is.
And knowing if you are sterile is a tough one -- you could be infertile/have low fertility, but actual sterility I think is rarer. It depends on why you would be infertile. Not having ovaries would be a big one that would rule out conceiving. Having PCOS could just make conception very very hard, and for some women, impossible. It's not quite cut and dried.