  We compute the lowest order gravitational UV divergent radiative corrections
to the S matrix element of the $fermion + fermion\rightarrow fermion + fermion$
scattering process in the massive Yukawa theory, coupled either to Unimodular
Gravity or to General Relativity. We show that both Unimodular Gravity and
General Relativity give rise to the same UV divergent contribution in
Dimensional Regularization. This is a nontrivial result, since in the classical
action of Unimodular Gravity coupled to the Yukawa theory, the graviton field
does not couple neither to the mass operator nor to the Yukawa operator. This
is unlike the General Relativity case. The agreement found points in the
direction that Unimodular Gravity and General Relativity give rise to the same
quantum theory when coupled to matter, as long as the Cosmological Constant
vanishes. Along the way we have come across another unexpected cancellation of
UV divergences for both Unimodular Gravity and General Relativity, resulting in
the UV finiteness of the one-loop and $\kappa g^2$ order of the vertex
involving two fermions and one graviton only.
