Yes they could but based on the special features that Criterion has been producing for years now, I feel very safe in saying that they won't.
EDIT: Just to be clear, I'm not knocking Criterion because the market is not what is was 10 or 15 years ago so they can't turn a profit if they produce a...
If there Isn't an old talk show or documentary with Otto Preminger or Frank Sinatra talking about the movie, the most Criterion would do today is include an interview with a film critic or two.