No, this will not happen in any meaningful way.
The NAU as a concept has been floated around in some circles, but it little more than an academic concept. I did some additional research for this answer, and found a neatly corroborating quote in wikipedia: "an academic exercise with pretensions of reaching policymakers"
The three countries will move towards some common ground as far as trade goes, but the NAU is simply not politically feasible for a variety of reasons.
There is no real popular support in any of the three countries for such a union.
I know of NO policymaker in any of the three countries who has decided to become a proponent of this idea. On the contrary, I can name several in the US who are violently opposed to it.
Further, one simply has to look at the difficulties in Europe in adopting the EU. Even in a more conducive environment there are still countries that have opted out of most of the EU provisions, and kept their currencies.
I currently see no trends in the US that hint of some sea change in attitude towards such a thing. I read several studies regarding such things for an international economics course, and the reality regarding such things is that countries as a whole, are disintegrating into smaller states.
BUT
The second part of your question has to do with ramifications:
That would be hard to guess at, because the real aspects of such a Union would vary widely.
Quite honestly, I couldn't see much that might change other than the adoption of a common currency.
Mexico already exports vast amounts of labor to the US, and such a Union would probably actually keep more Mexicans in Mexico, as living standards there would rise to the point where they would not have to migrate to make a decent living.
Canada would lose its national health care system. This is another reason I don't see Canadians jumping up and embracing a common union that would likely see the end of such a thing.
The average person in the US would see little result, other than a likely lowering of fuel prices, as the inefficient national oil company was privatized and oil production that Mexico controls would receive massive amounts of development capital from US companies seeking to profit from the oil that Mexico controls.