Usually the blue gene (Bl) is considered incmpletely dominant. Mostly because the presence of one gene shows. The presence of two blue genes gives the splash colour.
With recessive white (c) the presence of one gene is, for all intents & purposes, cannot be seen. It is only when both genes at that positio (locus) are recessive white that the bird will be white.
If one crosses a splash bird, two blue genes (Bl//BL), with a recessive white bird (c//c) the offspring will only inherit one recessive white &, being recessive, the gene will have no noticeable effect on the colour of the offspring. Thus the colour of other plumage colour genes inherited from the white parent will now also be a determining factor of the colour of the offspring.
At a guess, I'd think there is a good chance the offspring of such a cross might be blue.
If the splash parent also carried a recessive white gene there would then be about 50% white offspring.