No question about it. The issue up to this point against a character doing this is that the one PoV character is very new to this business and not yet skilled enough to handle herself in another's dream. The person who is actually dreaming has the ability to control the dream, even if most never realize it. Egwene entered Rhuarc's dream back in tFoH, but lost control quickly and found herself changing into his perception of her before Amys pulled her out. The only other time entering a dream has come up was her encounters with Gawyn, where the strength of his feelings towards her is too much for her to control or resist once she is inside his dream. For an experienced Dreamwalker, entering another's dream should not be a problem, particularly if they have no experience or training in dealing with such invasions. One such example was Rand's dream where Lanfear joined him for a swim and then Asmodean popped in to chide her for wasting his time. Later Lanfear reveals that it had been Rand's dream, not a fake dream she brought him to, as is implied Ba'alzamon did to the ta'veren in EotW.
The experience with Nakomi could easily have been sent by the Wise Ones for these reasons, as well as the ones you give.

Even without the wards, don't forget about his warder bonds. Since there is nothing to break or unravel with those (as Lanfear suggested she could do), he should be even more protected.


They take the same test a clan chief candidate takes, just as Rand did in tSR and Aviendha did off-camera in ToM.

Bair
Actually, that's a bit over-motivated. From day one, or actually before, since it is standard operating procedure for Wise Ones to do with an unmarried chief, the plan was to get Rand an Aiel wife. That was why they told Aviendha to hang around and listen to him (the teaching thing was an afterthought developed later when it became plain that her presence was suspicious given her obvious disdain for him), and what Sorilea meant when she told Cadsuane that she expected Rand to take what was offered if it looked pleasant. They wanted Aviendha to hang around Rand and pay attention to him so he would find her attractive, and they could nudge her if she was slow to reciprocate and soon the car'a'carn is not think of the Aiel as a strange and alien people, but rather he is thinking of his Aiel wife and children when he has to make decisions that will affect the fate of their people. By this point, anything they do regarding Rand and Aviendha is simply following a very old plan, and nothing to do with suddenly adjusting to the particular circumstances where only a loved one can affect him. In fact, from various clues we receive about Aviendha and the Wise Ones' perceptions of Rand, aside from the fact that they fell in love in spite of everything, Rand and Aviendha have unwittingly done all in their power to screw that plan up royally - rather than a plan they embarked upon recently, based on the circumstances with Rand's emotional state and seizing upon an opportunity afforded them by Aviendha's relationship, it was actually a generic plan decided upon before they knew the particular individuals involved, which was nearly ruined by the personal developments and peculiar circumstances of the individuals involved.