Background. Flux balance analysis (FBA) is widely used to simulate gene essentiality in genome-scale metabolic models (GEMs), and several studies have proposed using FBA-based combination simulations to predict antibiotic synergy. However, whether standard LP-based FBA can detect synergistic interactions between essential gene pairs -- as opposed to merely confirming individual gene essentiality -- has not been systematically evaluated at scale. This limitation is well-known theoretically but has not been quantified across multiple species models.  Methods. We performed 107,296 partial inhibition grid simulations across three ESKAPE pathogen GEMs (iML1515, iYS1720, iYL1228), systematically varying pairwise gene inhibition from 0% to 100% in 10% increments for all 39 curated essential genes. We then constructed an alternative machine learning (ML) pipeline that uses FBA-derived metabolic features (flux profiles, pathway membership, gene essentiality scores) combined with experimentally curated synergy labels from the literature. We curated 45 antibiotic combinations (28 synergistic, 10 antagonistic, 7 additive) spanning 17 target genes and 11 pathways, with Bliss independence scores extracted or estimated from published studies conducted under heterogeneous experimental conditions (Bliss scores are literature-derived, not directly measured in this work).  Results. The FBA partial inhibition grid yielded zero synergistic gene pairs across all three models. All 39 essential genes exhibited step-function dose-response behavior with alpha* = 1.00, a mathematically predictable consequence of LP sensitivity analysis. As a proof-of-concept alternative, an ML classifier combining pathway identity features and FBA-derived metabolic features achieved F1 = 0.847 and AUROC = 0.804 under gene-level GroupKFold cross-validation (Gradient Boosting, binary, n = 45). Permutation testing confirmed the signal exceeds chance (z = 2.58, p < 0.001), though this does not imply clinical predictive power. Feature ablation revealed that pathway identity contributed more than FBA metabolic features (pathway-only F1 = 0.828 vs. FBA-only F1 = 0.807), and removing ribosome-targeting combinations reduced AUROC to 0.627 (near random), indicating that the model's discrimination is largely driven by a single pathway subgroup. FBA feature coverage was limited: 71% of combinations contained at least one gene unmapped in iML1515, and the "gene mapping status" artifact ranked as the second most important feature.  Conclusions. We draw a distinction between FBA as a synergy calculator (directly computing Bliss scores from growth rates, which fails for essential gene pairs under LP) and FBA as a feature generator (providing metabolic context for supervised ML, which shows preliminary signal). The primary contribution is the systematic negative result for the former: standard LP-based FBA cannot compute antibiotic synergy for essential gene targets, confirmed across 107,296 simulations and three GEMs. As a secondary, proof-of-concept contribution, we show that pathway identity features combined with FBA-derived metabolic features yield exploratory signal in a small (n = 45), biased curated dataset, but the FBA feature contribution is modest and heavily confounded by incomplete gene-model mapping (71% unmapped). The "FBA as feature generator" concept requires validation on substantially larger standardized datasets with species-specific GEM feature extraction before the claim can be considered robust. All code and data are available under MIT license at https://github.com/shoo99/ai-drug-target.