Effective collaboration between embodied agents requires more than acting in a shared environment; it demands communication grounded in each agent's evolving understanding of the world. When agents can only partially observe their surroundings, coordination without communication is provably hard, but communication can, in principle, bridge this gap by allowing agents to share observations and align their world models. In this work, we examine whether LLM-based embodied agents actually realize the ability to communicate. We extend PARTNR, a benchmark for collaborative household robotics, with a natural-language dialogue channel that enables two agents with partial observability to communicate during task execution. To evaluate whether dialogue leads to genuine world-model alignment rather than superficial coordination, we propose a framework for measuring world-model alignment defined over per-agent world graphs: observation convergence (do private world models align over time?), information novelty (do messages convey what the partner lacks?), and belief-sensitive messaging (do agents model what their partner knows?). Our experiments across three LLMs reveal that dialogue reduces action conflicts 40 to 83 percentage points but degrades task success relative to silent coordination. Using our metrics, we characterize the gap between superficial coordination and genuine world-model alignment, and identify where current models fall on this spectrum.