There is a problem, though. Redonda is an uninhabited island officially part of Antigua and Barbuda. The "kingdom" is actually a line of literary authors who claim succession from Matthew Dowdy Shiell, a banker who claimed he was given the title of king by Queen Victoria. To make the claim even less solid is that there are a total of nine people claiming they are king.
The odds of the pub being recognized as a foreign embassy are slim to nill. However, one can never be sure because bureaucracies like the British Foreign Office are known for the rare colossus error (not going to happen, but would be cool).