Yes, but it will be very, very slow (think minutes for a not particularly large codebase), and probably contain mistakes. It's not at all comparable to refactoring tools like Jetbrains' rename tool.

The refactoring feature in Cursor barely works, unlike any Intellij products

Do any IDEs expose their features (like refactoring) as tools the AI can use? Would much prefer that over the LLM trying to figure it out.

I wouldn’t even want the LLM for a simple rename. Volar and TSLS seem to handle renames without issue, even across files and file types (eg Vue and Typescript)