There are legends that they accept outsiders, but by all evidence we have seen they are clan based and family oriented. In fact they have strong traditions that clearly get passed down through generations. Certainly they have a larger degree out "outside blood" than the Aiel of the waste, but that is not evidence that more than a handful of the Tuatha'an are runaways from other societies ... In fact given the general disdain the vast majority of the world has shown the Tuatha'an it seems highly unlikely that anyone would runaway to join them. Much like the Romani/Gypsy people the Tuatha'an are accused of just about anything that goes amiss when they pass through, including young people going missing.

I also see no evidence that there is no sense of servitude within thier community either. In every instance we have seen them they have shown their willingness to serve those around them and their own community. The scene in the TR when they strapped children to their backs is evidence to me that the Tuatha'an have a deeply ingrained sense of service to community. In addition their dedication to finding the Song shows that they have a dedicated task to which they claim service.

With that said, you are correct that the Tuatha'an did abandon their duty. But no more so than the Aiel of the Waste did... Perhaps less so as they seemingly adopted a new duty rather than following one task from one Aes Sedai. The Aiel of the waste abandoned the very core of what it meant to be Aiel by abandoning the Way.

Those who spoke the Prophesy would not have seen either of these groups as true Aiel. But given that each group holds pieces of the puzzle it seems likely that the remnant of a remnant must rediscover the ideology of the Way in order to survive.

The Prophesy likely served as a warning to the Aiel of the waste as their warrior culture puts them squarely at the center of conflict, but should the Light win TG there is a chance Aviendha's vision could still come true if some of her people, along with the Tuatha'an who survived the various wars after TG, accepted the Way of the Leaf. This group would not have been part of the Aiel as Aviendha saw them in her visions and could still have easliy fit into the Seanchan ruled world as we've seen that the Seanchan accept the Tuatha'an's ways without issue. Hell they could even be in service to the Empress if you really want to start extrapolating.

As the Aiel in Rands visions once said "The Aiel are the Way" ... So yes I believe the Prophesy is more wide spread than simply the Aiel of the Waste.