Only two things affect the synthesis of vitamin D, and those are the amount of UVB photons penetrating the skin and the person's age. See my previous answer for an explanation and citations.
So if we disregard age the only question becomes do light boxes supply adequate UVB to synthesize adequate vitamin D? From what I can tell from a review of the products out there, the answer is probably not. Lights adequate to treat SAD aren't adequate to generate vitamin D, and a light that supplied adequate UVB would be dangerous if misused.
But in my mind the final nail in the coffin for light therapy is this study:
All subjects receiving vitamin D improved in all outcome measures. The
phototherapy group showed no significant change in depression scale
measures. Vitamin D status improved in both groups (74% vitamin D
group, p < 0.005 and 36% phototherapy group, p < 0.01).
In short, although phototherapy improved vitamin D levels, it did so only half as well as supplements, and unlike supplements it had no effect on depression.