If the DAC in the card driving the CRT has 8 bits of resolution then, yes, it displays 256 shades of gray. (The new "neckboard" adopts the monitor to accept an analog signal instead of the simple digital on/off of the original circuitry.) One *could* argue, I suppose, that a simple 0v->MAX DAC setup might not produce 256 *useful* greys.

(The human eye responds non-linearly to brightness changes; a simple 256 step DAC with equally spaced divisions can give you "too many" dark and bright-white-ish grays that your eye really can't tell apart while leaving a few too few slots for subtle differences in the area of maximum sensitivity. More modern video systems employ various strategies for using gamma correction to put more steps where they're useful, but you can still sometimes perceive grayscale banding today.)