Deep learning (DL) models for natural language-to-code generation have become integral to modern software development pipelines. However, their heavy reliance on large amounts of data, often collected from unsanitized online sources, exposes them to data poisoning attacks, where adversaries inject malicious samples to subtly bias model behavior. Recent targeted attacks silently replace secure code with semantically equivalent but vulnerable implementations without relying on explicit triggers to launch the attack, making it especially hard for detection methods to distinguish clean from poisoned samples. We present a systematic study on the effectiveness of existing poisoning detection methods under this stealthy threat model. Specifically, we perform targeted poisoning on three DL models (CodeBERT, CodeT5+, AST-T5), and evaluate spectral signatures analysis, activation clustering, and static analysis as defenses. Our results show that all methods struggle to detect triggerless poisoning, with representation-based approaches failing to isolate poisoned samples and static analysis suffering false positives and false negatives, highlighting the need for more robust, trigger-independent defenses for AI-assisted code generation.