Large Language Models (LLMs) have shown significant potential in understanding human communication and interaction. However, their performance in the domain of child-inclusive interactions, including in clinical settings, remains less explored. In this work, we evaluate generic LLMs' ability to analyze child-adult dyadic interactions in a clinically relevant context involving children with ASD. Specifically, we explore LLMs in performing four tasks: classifying child-adult utterances, predicting engaged activities, recognizing language skills and understanding traits that are clinically relevant. Our evaluation shows that generic LLMs are highly capable of analyzing long and complex conversations in clinical observation sessions, often surpassing the performance of non-expert human evaluators. The results show their potential to segment interactions of interest, assist in language skills evaluation, identify engaged activities, and offer clinical-relevant context for assessments.