That's an interesting question. I've never thought about it or seen that taken into account (its not something we fit to when constraining cosmology)
I just looked around and LIGO has constrained Omega_GW < 1e-7 (they find no evidence, but that is the limit of their sensitivity). This is at least an order of magnitude smaller than Omega_Radiation and so will have a negligible effect on cosmology/total energy content.