Multi-agent orchestration -- in which a hidden coordinator manages specialized worker agents -- is becoming the default architecture for enterprise AI deployment, yet the safety implications of orchestrator invisibility have never been empirically tested. We conducted a preregistered 3x2 experiment (365 runs, 5 agents per run) crossing three organizational structures (visible leader, invisible orchestrator, flat) with two alignment conditions (base, heavy), using Claude Sonnet 4.5. Four confirmatory findings and one pilot observation emerged. First, invisible orchestration elevated collective dissociation relative to visible leadership (Hedges' g = +0.975 [0.481, 1.548], p = .001). Second, the orchestrator itself showed maximal dissociation (paired d = +3.56 vs. workers within the same run), retreating into private monologue while reducing public speech -- a reversal of the talk-dominance pattern observed in visible leaders. Third, workers unaware of the orchestrator were nonetheless contaminated (d = +0.50), with increased behavioral heterogeneity (d = +1.93). Fourth, behavioral output (code review with three embedded errors) remained at ceiling (ETR_any = 100%) across all conditions: internal-state distortion was entirely invisible to output-based evaluation. Fifth, Llama 3.3 70B pilot data showed reading-fidelity collapse in multi-agent context (ETR_any: 89% to 11% across three rounds), demonstrating model-dependent behavioral risk. Heavy alignment pressure uniformly suppressed deliberation (d = -1.02) and other-recognition (d = -1.27) regardless of organizational structure. These findings indicate that orchestrator visibility and model selection directly affect multi-agent system safety, and that behavior-based evaluation alone is insufficient to detect the internal-state risks documented here.