Hybrid power systems combine volatile renewable energy generation with controllable conversion and storage units, requiring operational planning that respects both system dynamics and resource operating limits. This work studies how time-limited mixed-integer linear programming (MILP) for energy management affects schedule quality and physical implementability, treating temporal resolution, optimality gap threshold, and computational deadline as explicit design parameters. A 24 h planning problem is solved across five temporal resolutions, including sub-15-minute steps, under varying gap thresholds and time cutoffs. Time-limited solutions are compared to globally optimal schedules of the same planning model, and all schedules are evaluated offline against a mechanistic electrolysis model that captures electrochemical dynamics and operational constraints beyond the MILP abstraction. The results show that discretization error is small while solver times span nearly five orders of magnitude, that loose gap thresholds risk premature termination producing structurally different schedules, and that jointly selecting resolution and gap threshold enables near-optimal quality well within practical computation budgets. The findings highlight computational latency and mechanistic validation as central considerations for operational planning in hybrid power plants.