Mental health disorders affect millions worldwide, and healthcare systems are increasingly overwhelmed by the volume of clinical data generated from electronic records, telemedicine platforms, and population-level screening programs. At the same time, the emergence of novel AI-based approaches in healthcare calls for intelligent frameworks capable of processing domain-specific unstructured clinical information while adapting to patient-specific needs. This paper proposes an agentic framework for building robust LLM-based pipelines, where each stage is encapsulated as a LangChain agent governed by explicit policies and proxy-guided evaluation. Stages are incrementally locked once validated, ensuring that later adaptations cannot overwrite configurations without demonstrated improvement. The proposed framework evolves from feature-level exploration, through proxy-based tuning and freeze/rollback mechanisms, to full orchestration by an Orchestrator Agent that coordinates preprocessing, retrieval, selection, diversity, threshold optimization, and decoding. A proof-of-concept in transcript-based depression detection demonstrates that the framework converges to stable configurations, such as cosine similarity, dynamic Top-k, and threshold 0.75, while controlling evaluation costs and avoiding regressions. These results highlight the potential of agentic AI to enable population-level mental health screening over large clinical datasets, addressing critical challenges in trustworthiness, reproducibility, and adaptability required in healthcare environments.