The color accuracy will probably be much more affected by your
printing loop than by the small difference between gray and white.
In any case, if the color balance is that critical, you will
probably have to make a small adjustment prior to printing, but
that's just for extremely accurate work. You printer calibration
(profiling) influences the colors much more than the small
difference between a white card and a gray card.
BTW, the fuction of white balance is pretty straight forward, and
that's why you can use either white or gray. A good gray card has
no color... it is just a subdued tone of white, and good gray cards
are expensive. The standard is Kodak. Anyway, the white balance
simply looks at the card, and measures the 'chrominance' (color)
channels of the image. It then subtracts whatever value it measured
from your photos as you take them. The 'luminance' (brightness)
channel is ignored. That's why there is little difference between
white and gray, they both look similar in the 'chrominance' channel
when they are both pure color.