No the benefit of a staining developer is that it is proportional to silver density so that the stain effect is greatest in the areas of greatest silver density. Therefore a staining developer will serve not only to increase overall negative contrast but also to increase local contrast in the areas of higher negative density (print highlight areas).
In the case of a staining developer that imparts a greenish stain (ABC and PMK) with VC materials the effects are counter to the desired result. We are increasing contrast with the stain effect but then we are decreasing contrast through the color of the stain. This occurs by the fact that the stain color acts as a variable contrast filtration factor in it's own right.
To decrease print highlight contrast would tend to lump the highlight values into a blocked condition at it's extreme condition. To increase highlight contrast is to separate highlight values into more definable values. I hope that I have expressed this clearly.