Modern software systems require code that is not only functional but also maintainable and well-structured. Although Large Language Models (LLMs) are increasingly used to automate software development, most studies focus on isolated, single-agent function-level generation. This work examines how process structure and role specialization shape multi-agent LLM workflows for class-level code generation. We simulate a Waterfall-style development cycle covering Requirement, Design, Implementation, and Testing using three LLMs (GPT-4o-mini, DeepSeek-Chat, and Claude-3.5-Haiku) on 100 Python tasks from the ClassEval benchmark. Our findings show that multi-agent workflows reorganize, rather than consistently enhance, model performance. Waterfall-style collaboration produces cleaner and more maintainable code but often reduces functional correctness (-37.8\% for GPT-4o-mini and -39.8\% for DeepSeek-Chat), with Claude-3.5-Haiku as a notable exception (+9.5\%). Importantly, process constraints shift failure characteristics: structural issues such as missing code decrease, while semantic and validation errors become more frequent. Among all stages, Testing exerts the strongest influence by improving verification coverage but also introducing new reasoning failures, whereas Requirement and Design have comparatively modest effects. Overall, this study provides empirical evidence that software process structure fundamentally alters how LLMs reason, collaborate, and fail, revealing inherent trade-offs between rigid workflow discipline and flexible problem-solving in multi-agent code generation.