If relativity hadn't predicted the precession of Mercury, would skeptics be obligated to study Einstein's proofs in detail anyway?

A thought occurred to me while commenting over at Jerry Coyne's blog, and I just want to give a more concise version here.

The equations underlying the theory of relativity are quite elegant and beautiful. A friend of mine tells me of a modern physics class he was taking where the students burst into applause when the professor finished the derivation of E=mc². So much complexity is summed up so simply and in such a cohesive theory.

This suggests that it might be true, but it's not evidence. One of the first solid pieces of evidence in favor of relativity was that it accurately predicted the precession of Mercury. And of course many more observations came later which confirmed the value of Einstein's theory over Newton's. One by one, the skeptics were forced to take Einstein's work seriously.

But let's imagine an alternate reality where relativity hadn't made this prediction, and in fact it's prediction for the orbits of all the other planets was somewhat less accurate than traditional Newtonian dynamics. Would a contemporary skeptic still have to take Einstein seriously? Would Einstein have been justified in saying, "You simply don't understand the math behind it. Look how elegant this equation is! Look how it unifies space and time in such a concise way! If you aren't convinced, I think you really need to read my book..."?

No he would not. And in a world where, it seems to me, the evidence against theism is overwhelming, we are under no compulsion to explore logical arguments for God. Arguments based on pure reason are often useful, but they ultimately carry very little to no evidential weight. I don't need to understand Aquinas' Five Ways in detail, or be able to point out the flaws in them, because I can just look around say, "Welp, no gods here. Must be some flaw in his reasoning or a concealed false assumption or something." Pure reason is valuable, but it has no power to convert the skeptic, nor should it. And that goes whether you are talking about science or theology.