I realize this site is primarily for questions and answers. However, assume for the sake of argument that a question was deleted for lack of interest (as sometimes happen) but an identical subject reemerged within the research community. Would it be possible to reference an old now-deleted question or is the question completely gone as far as Math.se is concerned?
It is almost impossible to find old, deleted questions if you're not a moderator unless you saved the link in the past. And users below 10k reputation can't see those questions anyway.
If you manage to find an old, relevant question and have the reputation to see it, you can quote it in your new question if that is useful. Quoting solves the issue that most users won't be able to see the original.
To answer this part of your question: Is the question completely gone as far as Math.se is concerned?
Deleted posts are usually not physically deleted (that is, removed from the system); they're just hidden (AKA soft-deleted). This means they won't appear in search results or data dumps, and normal users following links to them will see a 404 (not found) page.
Moderators, and normal users with >=10k reputation, see all deleted posts. Moderators are able to undelete any deleted post. "10kers" may vote to undelete deleted questions (it takes three votes to undelete), but cannot undelete deleted answers.