The GW approximation is known to violate causality, yielding self-energies with unphysical poles in the upper half of the complex frequency plane. The combined GW+DMFT approach attempts to cure this by injecting the exact local self-energy. Using exact diagonalization on minimal Hubbard clusters, we rigorously benchmark the analytic structure of the GW and GW+DMFT self-energies. We demonstrate a ``dimer anomaly'': on the two-site dimer, inversion symmetry forces the non-local self-energy to be purely real, masking the causality violation. Moving to the non-bipartite three-site Hubbard ring, where hopping frustration yields a finite imaginary part in the non-local self-energy, we prove that both GW and GW+DMFT violate the Matsubara causality condition. By analytically evaluating the exact Lehmann moments, we derive a closed-form expression for the high-frequency tail of the self-energy, C = U² Var(d) I, and show that standard methods fail to capture the exact equal-time two-particle correlators required to enforce it. The equal-time correlators that govern this tail are precisely those encoded in the high-frequency asymptotics of the fully irreducible vertex Λ; nevertheless, our intermediate-frequency analysis demonstrates that the local-only truncation of Λ in GW+DMFT leaves non-local RPA resonances uncorrected. The two diagnostics are logically independent: GW+DMFT satisfies the necessary high-frequency condition Csucceq0 yet still violates the Matsubara sign condition at finite frequencies. Taking the interpolation-free real-axis evaluation of the exact self-energy as the primary causality certificate, with rational continuation as supporting evidence, we establish a rigorous benchmark demonstrating that local self-energy corrections are insufficient to guarantee a causal analytic structure on frustrated clusters.