  We report the first Atacama large millimeter/submillimeter array observations
of MCG-03-58-007, a local ($z=0.03236\pm0.00002$, this work) AGN
($L_{AGN}\sim10^{45}~\rm erg~s^{-1}$), hosting a powerful X-ray ultra-fast
($v=0.1c$) outflow (UFO). The CO(1-0) line emission is observed across
$\sim18\,$kpc scales with a resolution of $\sim 1\,\rm kpc$. About 78\% of the
CO(1-0) luminosity traces a galaxy-size rotating disk. However, after
subtracting the emission due to such rotating disk, we detect with a S/N=20 a
residual emission in the central $\sim 4\,$kpc. Such residuals may trace a low
velocity ($v_{LOS}=170\,\rm km\,s^{-1}$) outflow. We compare the momentum rate
and kinetic power of such putative molecular outflow with that of the X-ray UFO
and find $\dot{P}_{out}/\dot{P}_{UFO}=0.3\pm0.2$ and
$\dot{E}_{mol}/\dot{E}_{UFO}\sim4\cdot10^{-3}$. This result is at odds with the
energy-conserving scenario suggested by the large momentum boosts measured in
some other molecular outflows. An alternative interpretation of the residual CO
emission would be a compact rotating structure, distinct from the main disk,
which would be a factor of $\sim10-100$ more extended and massive than typical
circumnuclear disks revealed in Seyferts. However, in both scenarios, our
results rule out the hypothesis of a momentum-boosted molecular outflow in this
AGN, despite the presence of a powerful X-ray UFO. [Abridged]
