Regardless of whatever way you look at both Neji and Tenten together, I think one of the things that really establish them, as a functional pair is their trust. It’s the foundation for something that can grow in the future. They trust each other because they remain truthful to themselves. It serves as their mechanism of growth. This is why I view the pairing/partnership/friendship to be so dynamic and interesting.
It does have its problems. Tenten didn’t handle Neji’s suffering properly, and Neji didn’t treat Tenten with respect, but that’s not to say that they’ve not improved from this since their genin days. They’ve both learned their own lessons, but they didn’t learn their lessons without the other’s aid. They’ve matured, learned, trained, and complained together. But it is the fact that they are still growing within their team that makes this relationship stable, but dynamically interesting.
Could it happen? Sure. What makes it so unlikely especially now in the time skip? Kishimoto spent time re-establishing the team dynamic, and emphasized the distinct interactions between the members of team Gai. Even now Tenten and Neji are more likely to communicate effectively and naturally with each other. And they do all of this in such a simple manner. I believe that they are able to interact this way because they are compatible. It’s even more natural for Tenten considering that her character design pulls on the fact that she is very adaptable. Compared to all the members of her team, Tenten is the most stable, and with someone like Neji who has his moments of instability, a character like hers is ideal to help him balance himself out. Tenten herself isn’t at all perfect at balancing since it’s been shown that she can lose her temper quickly, but that doesn’t mean Neji can’t be the one to ground her. It’s in these ways that they can learn to rely on each other, need each other. It strengthens them both individually, but helps keep their bond healthy and strong.
So yes, I made the pairing sound simplistic, but it really only stems off from these simple ideas into something more complex. Like I mentioned before, it does have its black and white areas around the gray, but those differences among the similarities that are present will help preserve the relationship. It’s one thing to be complete opposites, or completely identical with everything you do, but it’s another when there’s a perfect balance between these two ideas that something strong like Neji and Tenten’s relationship can truly flourish and change. It’s at this point where they can go to each other for strength, but at the same time be strong individuals as well. It’s that aspect of character strength that really makes this thing solid in my mind.
Feel free to add your own opinion if you want, or tell me I'm nuts. Whatever. XD