Let the inclination angle of the line $x\cos\alpha - y + 1 = 0$ be $\theta$, then $\tan\theta = \cos\alpha$,

Since $\cos\alpha \in [-1, 1]$,

Therefore, $-1 \leq \tan\theta \leq 1$.

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

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

By setting the inclination angle of the line $x\cos\alpha - y + 1 = 0$ as $\theta$, we obtain: $\tan\theta = \cos\alpha$. Given that $\cos\alpha \in [-1, 1]$, it follows that $-1 \leq \tan\theta \leq 1$. This leads to the conclusion.

This question examines the relationship between the inclination angle of a line and its slope, as well as the monotonicity of trigonometric functions, and is considered a basic question.