Text embeddings from Large Language Models (LLMs) have become foundational for numerous applications. However, these models typically operate on raw text, overlooking the rich structural information, such as hyperlinks or citations, that provides crucial context in many real-world datasets. This paper introduces and systematically evaluates a new paradigm for generating structure-aware text embeddings by integrating these structural relations directly into the LLM's internal encoding process, rather than relying on traditional post-hoc aggregation. We investigate two primary in-process methods: sequential concatenation and parallel caching. Through extensive zero-shot experiments across retrieval, clustering, classification, and recommendation tasks, we demonstrate that our structure-aware approaches consistently outperform both text-only and post-hoc baselines. Our analysis reveals critical trade-offs: sequential concatenation excels with noisy, moderate-length contexts, while parallel caching scales more effectively to long, high-signal contexts but is more susceptible to distractors. To address the challenge of noisy structural data, we also introduce and validate two effective techniques: Context Distillation and Semantic Balancing. This work provides the first comprehensive analysis of in-process structure-aware encoding, offering a blueprint for building more powerful and contextually aware embedding models.