No, van der Waals functionals would not be appropriate for this type of system - at least, not normally.
Most semiconductors of interest are strongly bonded 3D materials, with covalent bonds and perhaps a small polarisation (e.g. GaN). Semi-local exchange correlation methods describe these systems well, on the whole, with the exception of the well-known underestimation of the band-gap. The band-structures are usually modelled well, apart from the band-gap itself, so if you already know what the band-gap is, the simplest approach is just to correct the band-gap using a scissor operator.
Van der Waals functionals are designed to capture the non-local, long-range correlation of weakly-interacting densities, which is the mechanism for the van der Waals interaction. This interaction is important when modelling the energies and forces between atoms which are relatively isolated, for example inter-molecular forces, or the long-range interaction between a molecule and a surface. However, it is a subtle correlation effect with a fairly small interaction energy, and it is easily disrupted at short ranges and in the presence of other, stronger interactions. They could be relevant for bundles of loosely-coupled 1D (e.g. nanotubes) or 2D organic semiconductors (e.g. functionalised graphene), but they are extremely unlikely to be relevant for any conventional 3D semiconductors.
Since you are interested in band-gaps, I will also point out that van der Waals functionals do not address any of the issues relevant to predicting accurate band-gaps; for example, they do not contain the correct derivative discontinuity, they do not correct self-interaction, they do not lead to piecewise-linear energies as a function of band occupancy (Koopman's Theorem), and they do not give good values for the ionisation potential.