The Ark has long been a source of fascination in popular culture, a niche that was cemented for it by Raiders of the Lost Ark. It shows my ignorance, but I had no idea that the Ethiopian Orthodox Church claimed to have it in their possession. My first thought on reading that it had been there since the 1960's was to wonder where it had been between the Babylonian conquest and the sixties. However a quick bit of research tells me that the legend of the Ark being in Ethiopia goes back to at least the 12th Century AD.
That still leaves a lot of history unaccounted for, but wouldn't it be extraordinary if this could be shown to be the real thing? Such concrete evidence of First Temple Judaism would cause huge delight (and some dismay) in scholarly circles, not to mention the excitement that it would trigger in the religious world. Of course the temptation to open it to see whether it really contains Moses' stone tablets, Aaron's staff, and a pot of manna would be very strong. Although, since it was said that to touch it was certain death, that might complicate things slightly.
There is a strange paradox about this, though. Imagine that it could be demonstrated that the box in Axum was, in all probability, the same one that sat in Solomon's Temple. Would that make any difference whatsoever to the way in which we think about our faith, or would anybody, believer or unbeliever, become more convinced about the truth of Christianity or Judaism? I don't think it would. In the end, it isn't artefacts that lead people to faith, but something altogether less tangible.