No, because they are different variants of the same gene, and both are dominant over the regular, full-color-expressing gene. The white cat has to be where the black + white kitten got its white spotting from.
There are three basic options for white fur expression: full-color expression, white spotting (tuxedo, etc), and fully white. Each cat carries one of these genes from each parent.
Black Cat = 2 full color genes
White Cat = 1 fully-white gene, 1 white-spotting gene
Their kittens will all receive either the fully-white gene or the white-spotting gene from the cat. (This is the only way a black + white cat is possible with these parents.)
Statistically, 50% of their kittens are likely to be white, and 50% are likely to be white-spotting.