There are some people that received the title Sir who were not subjects of the British monarch - so you could be appointed , but this is not likely.
There is no distinction between a "regular" knighthood and "honorary" knighthood. It is perfectly acceptable for non-commonwealth citizens to be knighted, though they are unable to use the title "Sir" or "Dame" unless they become citizens of the British Empire.
http://archive.tivocommunity.com/tivo-vb/history/topic/156544-1.html
With regard to British knighthood, a person who is not a subject of the British monarch (i.e., a citizen of a non-Commonwealth realm) who receives an honorary knighthood is not entitled to use this style (e.g., Alan Greenspan, KBE, not Sir Alan Greenspan). Dual nationals holding a Commonwealth citizenship that recognises the British monarch as head of state are entitled to use the styling, although common usage varies from country to country: for instance, dual Bahamian-American citizen Sidney Poitier, knighted in 1974, is often styled Sir Sidney Poitier, particularly in connection with his official ambassadorial duties, although he himself rarely employs the title
http://en.wikipedia.org/wiki/Sir
Non-Commonwealth foreigners, however, may be made Honorary Members. For instance, two individuals were made Knights Grand Cross shortly after the conclusion of their terms as Presidents of the United States: Ronald Reagan (in 1989) and George H. W. Bush (in 1993), and one previously for his service as Supreme Allied Commander in World War II Dwight D. Eisenhower.
http://experts.about.com/e/o/or/order_of_the_bath.htm