According to the U.S. National Institutes of Health, more than 3.4 million children experience speech disorders that require clinical intervention. The number of speech-language pathologists (SLPs) is roughly twenty times fewer than the number of affected children, highlighting a significant gap in children's care and a pressing need for technological support that improves the productivity of SLPs. State-of-the-art multimodal language models (MLMs) hold a promise for supporting SLPs, as recent advances have demonstrated their ability to understand human speech patterns from audio inputs. Despite their potential, the use of MLMs in supporting SLPs remains underexplored, largely due to a limited holistic understanding of their performance in high-stakes clinical settings. To address this gap, we collaborate with domain experts to develop a taxonomy of real-world use cases of MLMs in speech-language pathologies. Based on our taxonomy, we introduce the first comprehensive benchmark that assesses the performance of LLMs on five core use cases, such as speech disorder diagnosis and symptom identification. For each use case, we manually label 1,000 data points to assess model performance. To further improve the performance of LLMs for SLPs, we fine-tune MLMs, enhancing performance across multiple tasks by more than 30\% over baseline models. We study the robustness and sensitivity of model performance under various settings, including background noise, speaker gender, and accent. Our evaluation of 15 state-of-the-art MLMs reveals that no single model consistently outperforms others across all tasks. Notably, we observe a performance disparity favoring male speakers and find that enabling reasoning may degrade performance. These findings highlight both the promise and limitations of current MLMs in speech-language pathology applications, underscoring the need for further research and targeted development.