Solution: From $x\sin\alpha - y + 1 = 0$, we find that the slope of this line is $\sin\alpha \in [-1, 1]$.

Let the inclination angle be $\theta$ ($0 \leq \theta < \pi$),

then $\tan\theta \in [-1, 1]$.

Therefore, $\theta \in [0, \frac{\pi}{4}] \cup [\frac{3\pi}{4}, \pi)$.

Hence, the correct choice is: $\boxed{D}$.

By deriving the range of the slope from the given equation of the line, and then using the slope as the tangent value of the inclination angle, we find the answer.

This question examines the inclination angle of a line, exploring the relationship between the inclination angle and the slope, and is a basic question.