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Hydrogen uptake in complex multicomponent alloys, including high-entropy alloys (HEAs), governs both hydrogen storage capacity and resistance to hydrogen-induced degradation. We combine high-pressure experiments, density-functional theory (DFT), and a GRACE universal interatomic potential to investigate hydrogen absorption in Al0.3CoCrFeNi and AlCoCrFeNi HEAs. In H as a pressure-transmitting medium, the FCC Al0.3CoCrFeNi alloy forms hydrides at ambient temperature above 3 GPa, whereas the Al-rich B2 AlCoCrFeNi alloy shows no evidence of hydride formation even upon heating at pressures up to 50 GPa. Experiments and calculations show that aluminum suppresses hydrogen uptake by increasing solution energies and destabilizing interstitial sites. The universal potential, employed in the calculations and pretrained on large DFT databases, closely reproduces DFT energetics and demonstrates transferability from the dilute limit to the hydride-forming regime. Simulations further disentangle the roles of local ordering, volume changes, composition, and crystal structure. Overall, our results indicate that hydrogen solubility in Al-containing HEAs is governed primarily by composition, with Al-driven B2 ordering as a strong secondary effect.