Does the sky darken proportionally during a partial solar eclipse?
Assuming the intensity of the sunlight is proportional to the area of the Sun which is showing, we can roughly calculate the intensity of sunlight, $I(d)$ as:
$$I(d) = 1 - \frac{\mathrm{Area}_{\mathrm{overlap}}}{\mathrm{Area}_{\mathrm{Sun}}}$$
Where $\mathrm{Area}_{\mathrm{overlap}}$ is the overlap between the Moon and the Sun (the green area).

(source: uga.edu)
Some calculation finds the overlap to be:
$$\mathrm{Area}_{\mathrm{overlap}} = 2r^2\cos^{-1}\left(\frac{d}{2r}\right) - \frac{d}{2}\sqrt{4r^2 - d^2}$$
Where $d$ is the distance between the centres of the Moon and the Sun. Similarly, the area of the Sun is:
$$\mathrm{Area}_{\mathrm{Sun}} = \pi r^2$$
Putting this together, you get the graph:

Where the Y axis is brightness (ranging from 100% to 0%) and the X axis is $d$ (ranging from $2r$ to $0$).
I hope this answers your question: the brightness does not change proportionally to coverage/time.
Note:
This assumes that $d$ increases linearly with time (the moon doesn't speed up or slow down as it moves across the Sun).