Yes, that's quite possibly the connection to Elayne that gifted Aviendha with this Talent.

It's fairly obvious this isn't over. Aviendha will be back, sooner than later probably (I expect her to go to Caemlyn soon after Rhuidean. She is eager to marry Rand, she needs to set it up with Elayne first, by her customs). It's even quite possible that by the end of TGS, Aviendha was already in Caemlyn. She's been away a very long time, for someone who needed to go to I forget-which-hold and walk to Rhuidean. She should have been gone perhaps 20 days, and she's been away for quite longer. That said, I'm fairly convinced something momentous or at least important happens between her and the Aiel living in Rhuidean, and has delayed her. I'm still fairly convinced, even more so with all the stuff about famine and refugees and war and the Aiel she mused over in TGS, that she's destined to the one to understand the value of the Da'shain's talent in a world like this. After Rand got over the Kinslaying and all, after he renounced hopelessness, it seems an extremely fitting moment to bring him the real "children of the dragon", and to bring back the crop songs (after Rand spoiled the reserves in TGS, beside). I think it's no coincidence right before their mutual "epiphanies" both Rand and Egwene were brought back to the Tinkers in their own way. Rand thought of the columns, Egwene of her time among them. All that seems missing in the picture is Aviendha's role in all of this. To the horror of many WO, quite possibly, I think she might be the one leading a return of the Aiel to the Way, and to service to the world (it's her whole "while should I feel this compassion for people when logic says their pain is of their own making why do I feel compassion even for people whose culture I loathe, why do I feel like I do about Olver? Etc.). Contrary to a lot of reader's views (not yours!), a major theme surrounding the Leafers has been their dependence as a burden to anyone they get close to (thankfully, they tended to stay away until recently), and their complete uselessness (yeah, they mend pots well... they don't have to live as they do for that). This has barely started to change, the Tinkers seem to feel very guilty of asking for protection and giving nothing in return. When they do approach people, they do seek ways to be useful. Aviendha's main theme has been the forsaking of the warrior ways to learn to become a non-violent Guide to others, to learn that real strength does not only come from the ability to defend yourself or commit violence. Aviendha is also obsessed with feeling useless since she's no longer a Maiden. She is also very afraid of weakness, and of Aes Sedai even. Even in TGS, the WO were still at the point of telling her "see, you're far from hapless - you're extremely talented etc.". She's by a long shot the Aiel character who seems the best positionned to suddenly turn everything aroun after an epiphany. That won't be the other WO, way too set in their ways, and that certainly won't come from the chiefs either. I think the WO may already know their hope resides with Aviendha, though. I would not be too surprised if they've known what had to be done from what the women see in the Columns that men don't (we should go through WO's history - we've barely see them in Rand's experience, mostly the male and female warrior paths), have been unable to take the steps (they're too afraid) and count on Aviendha to do it. Either that, or she'll surprise them by the way she interprets what needs to be done. But I think they know what's coming for them... they aren't preparing Aes Sedai for nothing - they know they'll be stuck with them again soon, and they are horrified by what these women are.

Aviendha has all the necessary ties: to Rand himself whose real relationship to the Da'shain as "children of the dragon" n the WOS is still mysterious, to all the right themes, to the Amyrlin Seat who wish to tie the WO to the WT (Egwene might have to settle for all the Aiel...), to Elayne... And then there's the "treasure" bit. Rhuidean holds some of the secrets of the Dai'shain's songs, but it won't teach them. Rand may or not have the Voice. It's not because da'shain had free access to his house that he does sing himself. If he doesn't, as seems likely (he wasn't, after all, a Da'shain Aiel), then the best hope is in Elayne's music box.

The major component Aviendha misses is the Tinkers/the Way. But Jordan seems to have taken care of that long ago. When Rand broke the Aiel, we were told there were many more Tinkers than usual in the Waste and many of those touched by the bleakness have gone to ask them to take them in. By the time Aviendha gets to Rhuidean, there might already be tons of caravans of Tinkers there, and Aiel living the Way again. Aviendha might go into the Columns appalled by what she saw of the Aiel in and around Rhuidean, and fearful of what she'll see (she knows the gist of it... but not the details), and come out of there knowing what she must do next with these people.

As for the collection in Caemlyn, there seems to be a bit of everything in there: important plot devices, red herrings, stuff that won't serve before the epilogue (I suspect this is the fate of the Library. It's too much a deus ex machina to be used in the LB, IMO). Heck, there even seems to be a ter'angreal there that might be used to test the power of Singing (not necessarily doing anything useful to the plot, beside proving the Aiel have the Voice right). I think the important one might be the music box, and the dagger (contrary to a lot of people's opinion, I'm fairly convinced the device isn't for Rand as SG, it's for Mat in TOM. The dagger is the reason why Elayne hasn't been attacked by the gholam yet, but when she learns Mat is pursued by the Shadow, Elayne will insist Mat take the dagger (will she bring back the "by Min's viewing, nothing can happen to me" routine? Quite possibly), which he will refuse. They're gonna fight over which of them ought to have that dagger. Mat will end up with it (it might insist on Elayne having the medallion, then). Totally Jordan-like to get Mat a new dagger to travel back to Whitebridge. Incidentally... the dull dagger is made of iron. "Iron to bind" is one of the things Mat must bring into the Tower of Ghenjei to cheat the Finns.