I am confused by your terminology. Culturing more yeast from a White Labs vial is the same as making a starter. The starter procedure for a mead is no different than a starter for anything else, the main goal is to grow more cells, and to grow enough of them to handle the specific gravity they are pitched into.
Using yeast cells from a previous batch repeatedly, can result in off-flavor after multiple generations, but that depends on the conditions of the beers and the yeast strain itself. Many people create a "stock" culture from the original. Each time the yeast will be used, a vial of stock culture is stepped up in starters, instead of reusing/washing yeast from a batch. It is unnecessary to continuously grow the yeast unless you use it often. You can do this by growing cells in the starter, crashing them out, decanting off the spent wort, and adding new wort to keep the cells growing.