Large-language-model code generation has shifted from single-shot prompting to multi-agent orchestrations - analyst, coder, tester, and debugger pipelines - and is evaluated almost exclusively on functional correctness. Whether these architectures also affect the structural complexity of the code they produce, and which orchestration layers carry the cost, remains largely unexamined: prior work has documented prompt-level effects on code complexity, but the architecture-level question is open. We compare six widely-used multi-agent configurations (Basic, AC, ACT, Debugger, AC+Debugger, ACT+Debugger) under two models from the GPT-4o family across all 164 HumanEval tasks - 1,968 paired observations - using the five RADON complexity metrics (SLOC, cyclomatic complexity, and Halstead Volume, Difficulty, and Effort). We apply a paired non-parametric statistical pipeline (Friedman omnibus, Wilcoxon signed-rank post-hoc with Holm correction, Kendall's $W$ and matched-pairs rank-biserial effect sizes) in both all-completions and passing-only conditions. The six architectures collapse into two indistinguishable complexity clusters separated by a 50-130% gap, the same partition in both models and under both conditions; among the architectural layers, the analyst-coder split inflates complexity, the runtime debugger does not - and on the analyst-coder background actively deflates it - and the tester re-inflates it. The heavy cluster's additional complexity buys no pass@1 advantage: the leanest architectures match or beat the heaviest on accuracy. Architectural elaboration in LLM code generation should therefore be justified by measured benefit on the dimensions that matter, not assumed.