[@Ezmeralda] I do, and a Yellow would not be sent to retrieve something like that. That would likely be the duty of a Blue, or a Brown, depending on the circumstance.

Read more about Healing here, since they explained it really well: http://13depository.blogspot.com/2002/02/weaves-and-talents.html

This is the passage that interests me the most:

[quote]Complex Five Powers Healing

Unlike in the simpler forms of Healing, different weaves are used to Heal different illnesses. It takes longer, but all the strength comes from the Power and not from the patient and Healer. This is the Healing used during the Age of Legends, and men were better than women at some kinds of Healing (Lord of Chaos, Prologue). Flinn and a few other men can use the Power to remove deeply embedded objects (The Path of Daggers, Fog of War, Storm of Battle). 

The channeller can choose to Heal one particular condition and leave everything else as it was (Crossroads of Twilight, Glimmers of the Pattern). This complex Healing can even cure insanity to a limited degree (The Eye of the World, Prologue), but psychiatrists were probably preferred to treat most patients (Lord of Chaos, Threads Woven of Shadow). 

During Healing, the patient feels both hot and cold at the same time (The Dragon Reborn, Threads in the Pattern), perhaps due to the presence of Fire and Water in the weave. 
[/quote]

In other words, yes, standard simple healing and delving can be learned, but the complex healing- for which the Yellow Ajah is known- is much more involved than just one weave that can be applied to any situation. Every single ailment, injury, illness, what have you, has a different weave, and is dependent on the patient. It takes years of practice and a full understanding of the human body and the different things that can affect it.

You've got to remember that during the Trolloc Wars, people- Aes Sedai especially- remember the wonders of the Age of Legends, and they try to uphold them still. And I would expect that that would hold true in the Yellow Ajah, that they would train their Aes Sedai in all known permutations of the complex Healing weaves.

This is an instance of me saying no, by the way. If your Aes Sedai is 31, and of the Yellow or Green Ajah, then she will be confined to the White Tower.