Text-to-SQL systems have achieved strong performance on English benchmarks, yet their behavior in morphologically rich, low-resource languages remains largely unexplored. We introduce BIRDTurk, the first Turkish adaptation of the BIRD benchmark, constructed through a controlled translation pipeline that adapts schema identifiers to Turkish while strictly preserving the logical structure and execution semantics of SQL queries and databases. Translation quality is validated on a sample size determined by the Central Limit Theorem to ensure 95% confidence, achieving 98.15% accuracy on human-evaluated samples. Using BIRDTurk, we evaluate inference-based prompting, agentic multi-stage reasoning, and supervised fine-tuning. Our results reveal that Turkish introduces consistent performance degradation, driven by both structural linguistic divergence and underrepresentation in LLM pretraining, while agentic reasoning demonstrates stronger cross-lingual robustness. Supervised fine-tuning remains challenging for standard multilingual baselines but scales effectively with modern instruction-tuned models. BIRDTurk provides a controlled testbed for cross-lingual Text-to-SQL evaluation under realistic database conditions. We release the training and development splits to support future research.