No, it does not. It runs whatever EDITOR is set to (technically the first set of SUDO_EDITOR, VISUAL, and EDITOR).
> So presumably that means that it will have my environment, e.g. will run my .vimrc?
That is correct.
> Though that could be an attack vector too.
Only on the specific file, which would usually be a lot more noticeable unless the attack specifically manages to recognise and target sudoedited files while closing the buffer.