Recommender systems alleviate information overload, yet repeated feedback between recommendations and user interactions can reinforce existing preferences and narrow users' exposure, forming information cocoons. While this phenomenon has been widely studied in traditional sequential recommendation, its impact on generative recommendation remains unclear. By replacing atomic item IDs with Semantic ID (SID) sequences, generative recommenders introduce a different recommendation mechanism whose role in information cocoon formation is not yet understood. To investigate whether generative recommenders deepen information cocoons, we propose \textsc{RecLoop}, a closed-loop simulation framework with LLM-driven user agents. We compare two generative recommenders and two traditional sequential baselines on two Amazon datasets across multiple feedback cycles. In addition to standard exposure-level metrics, we introduce \emph{Code-Space Structural Cocoon}, a model-level metric that measures concentration in the generated SID space. Experimental results show that generative recommenders are generally less prone to exposure-level cocoon formation than traditional baselines, preserving broader exposure diversity and slowing cross-user homogenization. However, feedback loops can still induce concentration within the generated SID space. We further find that cocoon severity depends strongly on tokenization strategy and model scale: collaborative-signal tokenization produces stronger cocoon effects than semantic tokenization, whereas larger models maintain greater code-space diversity and better retain access to niche content. These findings suggest that information cocoons in generative recommendation are shaped not only by recommendation behavior, but also by item tokenization and model capacity. Our code is available at https://github.com/Dregen-Yor/RecLoop.

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