Can vital wheat gluten be added to white whole wheat pasta dough recipes?

Unless the flour you are using is specially made, all flours contain gluten. Bread flours generally contain added gluten, so when you supplement all-purpose flour with your own essential gluten protein, you are making it into bread flour. Whole wheat, rye -- it matters not. Gluten is what holds a dough together when it is under stress during bread making. Now, whether you should add it to pasta dough or not is another matter. Pasta is basically soggy, unleavened bread. Since you're not trying to make it rise, there wouldn't be any use in trying to fortify its ability to make gluten strands.