Will greenboard retard mold growth?
Greenboard is sheetrock where the paper is water resistant (but not necessarily water proof). A better alternative to greenboard is to use a paperless sheetrock product like Densarmor, which uses a fiberglass backing rather than paper (it's the paper that mold likes).

Note that these products aren't designed for wet applications, however. At best, they are designed for areas that 'are sometimes damp'. If you have mold issues under your sink, the problem is water. You have a leak somewhere. That has to be fixed. Replacing the sheetrock--even with one of these other products is just a bandaid and the problem will return if the leak isn't fixed.