No. (For the directions of vectors as given by you.)

TL;DR - You must measure the angle between two vectors, as per vector rules (extrapolating one to intersect the other and measuring the inner angle contained between the two vectors. By inner angle, I mean the one as seen from the side where both the vectors diverge from the point of intersection.)

Let us consider the following two pairs -

1. [math]\vec{u}.\vec{v}[/math]

The inner angle between the vectors, [math]\theta = [/math][math]\frac{\pi}{3}[/math]

The dot product in this case is [math]+\frac{1}{2}[/math] (assuming[math] ||\vec{u}|| = 1[/math])

2.[math] [/math][math]\vec{u}.\vec{w}[/math]

The inner angle between the vectors, [math]\theta = [/math][math]\frac{2\pi}{3}[/math]

The dot product in this case is[math] -\frac{1}{2}[/math]

Intuitively, dot product measures the degree of overlap between various components of the two vectors.

For the case of 1, there is a positive overlap in the directions of the non-zero components (only x) in both the vectors.

And for the case 2, there is a negative overlap, with both the vectors having directions opposite to one another in components with non-zero magnitude.

Lets align [math]\vec{u}[/math] along the [math]x[/math] axis, assuming it to have originated from the origin [math](0, 0)[/math].

(The python code for this plot can be obtained here, if interested)

Now [math]\vec{u}[/math] moves in the [math]+x[/math] direction with a unit magnitude, but has 0 magnitude of movement along the [math]y[/math]-axis.

[math]\vec{v}[/math] moves in the [math]+x[/math] with a magnitude of [math]\cos([/math][math]\frac{\pi}{3}[/math][math]) = 0.5[/math], and also in the [math]+y[/math] with a magnitude of [math]\sin([/math][math]\frac{\pi}{3}).[/math]

[math]\vec{w}[/math] moves in the [math]-x[/math] direction with a magnitude of [math]\cos(\frac{\pi}{3}) = 0.5[/math] and also in the [math]+y[/math] direction with a magnitude of [math]\sin(\frac{\pi}{3}).[/math]

Now comparing [math]\vec{u}[/math] with [math]\vec{v}[/math], we can see that the resultant overlap along [math]y[/math] is 0, however the resultant overlap along x is the product of two individual components [math]1 * \cos(\frac{\pi}{3}) = 0.5[/math]

However with [math]\vec{w}[/math], there is a negative overlap (the directions are opposite to one another) along the [math]x[/math] direction by a magnitude equal to [math]\cos\frac{\pi}{3} = 0.5[/math], but with a negative sign to denote that [math]\vec{w}[/math] and [math]\vec{v}[/math] move in opposite directions). (Net overlap along the [math]y[/math]-axis is 0 as before).