This is a very interesting idea and exactly one of these areas, where games have a huge potential.
I think in a RPG (or even a shooter) it will always increase the players involvement, if he feels recognized, if there is some attention from others.
Something similar (but without any further functionality) was implemented for example in Oblivion, where the NPCs turned to my player, when he was just passing. Especially in the beginning, when I started the game, this gave me motivation to turn to the NPC and start a conversation. However later in the game it felt more like another mechanical event also a little bit exaggerated.

I would probably try to create some kind of hierarchy in social interaction. Here´s just an example:

1) More decorative, than functional: Some NPCs look at your model more or less often, for this or that reason ( because you just became more famous, because you wear some expensive clothes). This just gives the player a feeling: I´m there. My life makes sense.

2) NPC looking at a player for an unusual long time: This is an indication, that this NPC has something to offer, or is of particular interest, depending on the story, but the NPC is too shy to talk directly to the player.

3) NPC directly talks to the player, turning into the archetype of a herald, giving for example information, that is essential for the storyline. In a certain way this is the storytellers equivalent of a mouse click.

In addition to that you could use facial expressions on the NPCs, making this behaviour more nuanced. A long look can mean completely different things ...

In the background there might be some numbers increasing or decreasing on the part of the NPC´s, which determine their general attitude towards your player and the functionality of the storyline. There could be a short term system, like in your example with the marble and the paint.
However simply looking around shouldn´t be too functional. I think it doesn´t have to be the only way of social interaction. A mouse click is still more clear and I would prefer a mouse click, if I want directly to turn to someone.
The looks should be reserved for subtle, more subconscious approaches.
I wouldn´t like a gameplay, where I have to read in a manual: look three times in the direction of the NPC, then his hand will automatically extend ...
So I think, your example works great in the beginning, but then maybe it makes things more complicated and I would probably use a more direct approach (traditional mouse click, followed by a dialogue tree).
I agree with Phemox. I think these subtle, psychological elements can make a huge difference, but I think you have to deliver them in many variations and in a good balance, because it can be very stupid if something subtle and psychological is implemented in a way, that looks and feels mechanical ...