Are you sure you aren't thinking of Vault 15? Vault 13 has very little to do with NCR besides the Vault Dweller. I also don't see how it is implied that the Chosen One sold the location to Tandi. She does ask if you found it. I don't recall the conversation off the top of my head. I don't think its canon that NCR found it.
Could be that Vault 13 went back to being a legend after the Chosen One went off to found New Arroyo. If NCR did find it and I don't see any real reason why then haven't. It could just be town, military base or storage area or maybe they just looted it.
No, it is an important role in NCR, more specifically, Shady Sands' history. They know he came from Vault 13, saved SS from certain doom, and vanished like smoke in the wind. In Fallout 2, it's pretty heavily implied that Tandi, while not mentioning it publicly lest being ridiculed for chasing 'fairy tales', is desperately looking for SOME proof of it. Plus, there is a conversation, I think it's like 3,000 gold coins and you'd sell her the location of Vault 13. I mean, I dont mean it's definitive canon proof, but for 3k just to point out the location of an empty Vault? I'd do that, it's not dishonest or evil, just business.
@Enclave- My memory is a little shaky, but from memory it was mixed with a wide range of various races (Hence Aradesh's accent) and the clashes culturally caused tensions to a boil until one group said 'eff this, we're leaving the Vault and taking the G.E.C.K. with us.' The Khans too are descended from Vault 15 dwellers.