Hybrid search has emerged as a promising paradigm that combines lexical and semantic retrieval, enhancing accuracy for applications such as recommendations, information retrieval, and Retrieval-Augmented Generation. However, existing methods are constrained by a trilemma: they sacrifice flexibility for efficiency, suffer from accuracy degradation, or incur prohibitive storage overhead for flexible combinations of retrieval paths. This paper introduces Allan-Poe, a novel all-in-one graph index accelerated by GPUs for efficient hybrid search. We first analyze the limitations of existing retrieval paradigms and extract key design principles for an effective hybrid index. Guided by the principles, we architect a unified graph-based index that flexibly integrates three retrieval paths (dense vector, sparse vector, and full-text) within a single, cohesive structure. To enable efficient construction, we design a GPU-accelerated pipeline featuring a warp-level hybrid distance kernel, RNG-IP joint pruning, and keyword-aware neighbor recycling. For query processing, we introduce a dynamic fusion framework that supports any combination of retrieval paths and weights without index reconstruction, flexibly leveraging logical structures from the knowledge graph to resolve complex multi-hop queries. Extensive experiments on 6 real-world datasets demonstrate that Allan-Poe achieves superior end-to-end query accuracy and outperforms state-of-the-art methods by 1.5x-186.4x in throughput, while significantly reducing storage overhead.