Can We Trust LLMs for Mental Health Screening? Consistency, ASR Robustness, and Evidence Faithfulness

LLMs can estimate Hospital Anxiety and Depression Scale (HADS) scores from speech in a zero-shot manner, but clinical deployment requires reliability across three dimensions: intra-model consistency, ASR robustness, and evidence faithfulness. We evaluate three LLMs (Phi-4, Gemma-2-9B, and Llama-3.1-8B) on 111 English-speaking participants using ground-truth transcripts and three Whisper ASR variants (Large, Medium, Small), with three independent runs per model-condition pair. We find that (i) Phi-4 and Gemma-2-9B achieve excellent intra-model consistency (ICC > 0.89) with minimal degradation under ASR; (ii) Llama-3.1-8B shows ASR-fragile consistency, with ICC dropping from 0.82 to 0.36 at 10% WER; (iii) predictive validity is largely preserved under ASR for robust models; and (iv) keyword groundedness exceeds 93% for Phi-4 and Gemma-2-9B but falls to 77-81% for Llama-3.1-8B. Inter-model keyword agreement is far lower than score-level agreement, revealing a score-evidence dissociation with implications for clinical interpretability.