We present Atacama Large Millimetre/submillimetre Array (ALMA) CO(1–0) observations of the nearby infrared luminous (LIRG) galaxy pair IRAS 05054+1718 (also known as CGCG 468-002), as well as a new analysis of X-ray data of this source collected between 2012 and 2021 using the Nuclear Spectroscopic Telescope Array (NuSTAR), Swift, and the XMM-Newton satellites. The western component of the pair, NED01, hosts a Seyfert 1.9 nucleus that is responsible for launching a powerful X-ray ultra-fast outflow (UFO). Our X-ray spectral analysis suggests that the UFO could be variable or multi-component in velocity, ranging from v/c ∼ −0.12 (as seen in Swift) to v/c ∼ −0.23 (as seen in NuSTAR), and constrains its momentum flux to be ṗoutX−ray ∼ (4 ± 2) × 1034 g cm s−2. The ALMA CO(1–0) observations, obtained with an angular resolution of 2.2″, although targeting mainly NED01, also include the eastern component of the pair, NED02, a less-studied LIRG with no clear evidence of an active galactic nucleus (AGN). We study the CO(1–0) kinematics in the two galaxies using the 3D-BAROLO code. In both sources we can model the bulk of the CO(1–0) emission with rotating disks and, after subtracting the best-fit models, we detect compact residual emission at S/N = 15 within ∼3 kpc of the centre. A molecular outflow in NED01, if present, cannot be brighter than such residuals, implying an upper limit on its outflow rate of Ṁoutmol ≲ 19 ± 14 M⊙ yr−1 and on its momentum rate of ṗoutmol ≲ (2.7 ± 2.4) × 1034 g cm s−1. Combined with the revised energetics of the X-ray wind, we derive an upper limit on the momentum rate ratio of ṗoutmol/ṗoutX−ray < 0.67. We discuss these results in the context of the expectations of AGN feedback models, and we propose that the X-ray disk wind in NED01 has not significantly impacted the molecular gas reservoir (yet), and we can constrain its effect to be much smaller than expectations of AGN ‘energy-driven’ feedback models. We also consider and discuss the hypothesis of asymmetries of the molecular disk not properly captured by the 3D-BAROLO code. Our results highlight the challenges in testing the predictions of popular AGN disk-wind feedback theories, even in the presence of good-quality multi-wavelength observations.