Traditional Automated Speaking Assessment (ASA) systems exhibit inherent modality limitations: text-based approaches lack acoustic information while audio-based methods miss semantic context. Multimodal Large Language Models (MLLM) offer unprecedented opportunities for comprehensive ASA by simultaneously processing audio and text within unified frameworks. This paper presents a very first systematic study of MLLM for comprehensive ASA, demonstrating the superior performance of MLLM across the aspects of content and language use . However, assessment on the delivery aspect reveals unique challenges, which is deemed to require specialized training strategies. We thus propose Speech-First Multimodal Training (SFMT), leveraging a curriculum learning principle to establish more robust modeling foundations of speech before cross-modal synergetic fusion. A series of experiments on a benchmark dataset show MLLM-based systems can elevate the holistic assessment performance from a PCC value of 0.783 to 0.846. In particular, SFMT excels in the evaluation of the delivery aspect, achieving an absolute accuracy improvement of 4% over conventional training approaches, which also paves a new avenue for ASA.