It's possible to work with these sample sizes using survival analysis, but I doubt Bayes would find the difference even with a really well initialized prior. I don't think that traditional significance testing is the answer here, those require even larger sample sizes (b/c you're not limiting the space of the estimate). It's all about limiting the domain-space. You know conversion rates are never over 10% on your homepage, why would you not exclude that to give your statistical work more power? That's at least how I think about it.