In his book, Mr. Ingram states that non-duality models of awakening are "without doubt [his] favorite of them all." As indicated by Mr. Ingram, there aren't specific moral changes in a non-dually awakened person's capabilities (i.e. not being able to lie) or experience (not feeling sensual desire). I've watched youtube videos of a couple other people who claim non-dual awakening, such as Jeff Foster: http://www.youtube.com/watch?v=XCGqQNUD2Dw
All of these people say that nothing really changes outwardly, except that there is a sort of disassociation
from oneself. For my own part I haven't done much thinking about nibbana, but two descriptions stick out to me from the canon: the cutting of the fetters, and completion of one's task in this life.
There is one way of thinking about the fetters: cutting the fetter of ill will means that one no longer experiences ill will. Another way of thinking about it is that ill will can arise, but that one isn't attached (fettered) to the ill will, as if someone else is experiencing the ill will. I don't know for myself. I guess either interpretation sounds both reasonable and unreasonable to me.
As for completing one's task in life, it seems that the Buddha still did things and made mistakes (for example, gave Vinaya rules which were later repealed by himself) after his enlightenment. Mr. Ingram certainly makes it clear that living in the world, and sila practice in general, is still as tough as it was before his awakening.
I have to admit that I'd be a little disappointed if enlightenment was only the kind of disassociation from one's self that is expressed by Jeff Foster (although he seems like a nice person!). It also seems to me that there are far easier ways to non-dual awakening than the Buddhist way.
Mr. Ingram's method of choice is vipassana meditation. I personally am a little hesitant to practice vipassana, because I can't find its source in the suttas and when I consider the method conceptually it seems that it leads precisely to the non-dual awakening mentioned above.
Couldn't the Buddha have just given Right Noting as the path and Non-Duality as his description of nibbana, if things were so simple (and had so few consequences)?