Have any GU graduates won a Nobel Prize?

It does not appear so. However, we have awarded honorary degrees to at least eleven Nobel Laureates:

Christian Anfinsen (Nobel Prize in Chemistry, 1972);
Oscar Arias-Sánchez (Peace, 1987);
John Bardeen (Physics, 1956 & 1972);
William Fowler (Physics, 1983);
Corneille Heymans (Physiology or Medicine, 1938);
Frank B. Kellogg (Peace, 1929);
Barbara McClintock (Physiology or Medicine, 1983);
Mohamed Anwar el Sadat (Peace, 1978);
Glenn Seaborg (Chemistry, 1951);
Mother Teresa (Peace, 1979);
and Elie Wiesel (Peace, 1986).

A twelfth Laureate, Robert Richardson (Physics, 1996), has a somewhat different Georgetown connection—he was born in the University Hospital.