Bacon Rib is actually made from a specialty cut, at least specialty in the US, typically called a belly rib cut. It is a full rack, and full belly. I have not had it cured, but just like bacon I would assume it could be prepared either cures or fresh. Typically it would be smoked for as long as 18 hours. Then the ribs would be cut, again with the belly still in place, and used for the final dish. Boiled with vegetables and cabbage is one typical route, or trimming up ribs to make them look nice and sauteing them and making a sauce with the drippings. I cannot say how common doing a full cure is, I have seen them served only a couple times and those were smoked but not cured. That however was in the US, and traditional Irish might have different tendencies.