"Did the leeches work?"
Nope. They did little good, and often much harm. The "bleeding" cure is only useful in Polycythemia Vera, a disease where the body creates too many red blood cells. It's rare, and it's unlikely that Washington had it.
Beyond Bloodletting:
FDA Gives Leeches a Medical Makeover
http://www.fda.gov/fdac/features/2004/504_leech.html
Reading before the College of Physicians in Philadelphia in 1932, Fielding O Lewis5 also entertained the diagnosis of "acute edema of the larynx, secondary to a septic sore throat of a probable streptococci variety." In 1936, Creighton Barker6 published an analysis offering a similar diagnosis: "a virulent streptococcal infection of the pharynx, with cellulitis in the walls of the hypopharynx and edema of the glottis." In 1942, Willius and Keys1 considered membranous croup, acute laryngitis, and Ludwig's angina and concluded: "The modern American physician in all probability would execute the certificate of death in the following manner: septic sore throat, probably of streptococcic origin, associated with acute edema of the larynx."
http://xnet.kp.org/permanentejournal/spring04/time.html
There isn't always a simple answer and to pretend otherwise is, what would you say - a lie?