The rapid advancement of Audio Large Language Models (ALMs), driven by Neural Audio Codecs (NACs), has led to the emergence of highly realistic speech deepfakes, commonly referred to as CodecFakes (CFs). Consequently, CF detection has attracted increasing attention from the research community. However, existing studies predominantly focus on English or Chinese, leaving the vulnerability of Indic languages largely unexplored. To bridge this gap, we introduce Indic-CodecFake (ICF) dataset, the first large-scale benchmark comprising real and NAC-synthesized speech across multiple Indic languages, diverse speaker profiles, and multiple NAC types. We use IndicSUPERB as the real speech corpus for generation of ICF dataset. Our experiments demonstrate that state-of-the-art (SOTA) CF detectors trained on English-centric datasets fail to generalize to ICF, underscoring the challenges posed by phonetic diversity and prosodic variability in Indic speech. Further, we present systematic evaluation of SOTA ALMs in a zero-shot setting on ICF dataset. We evaluate these ALMs as they have shown effectiveness for different speech tasks. However, our findings reveal that current ALMs exhibit consistently poor performance. To address this, we propose SATYAM, a novel hyperbolic ALM tailored for CF detection in Indic languages. SATYAM integrates semantic representations from Whisper and prosodic representations from TRILLsson using through Bhattacharya distance in hyperbolic space and subsequently performs the same alignment procedure between the fused speech representation and an input conditioning prompt. This dual-stage fusion framework enables SATYAM to effectively model hierarchical relationships both within speech (semantic-prosodic) and across modalities (speech-text). Extensive evaluations show that SATYAM consistently outperforms competitive end-to-end and ALM-based baselines on the ICF benchmark.