It seems so. According to a reference in the University Archives, the U.S. Government entered into an agreement with Georgetown College on June 13, 1838 to supply the College Cadets with Sixty short flintlock muskets. The caveat, though, was that in order to receive the muskets the Cadets had to become a volunteer militia. This agreement, titled "Regulations for the issue of arms to the Militia of the District of Columbia," is a part of Record Group 156 at the National Archives.
This first group of Cadets fizzled out and reformed in a more organized fashion in 1852. It is not clear what happened to the rifles or the Cadets' Militia status during their time of inactivity; however, it appears that the Cadets and the Government entered into other munitions agreements. Late 19th century correspondence between Georgetown President J. Havens Richards, S.J. and the War Department's Ordnance Office regarding rifles on loan to Georgetown can be found in the University Archives.
Georgetown's Charles Denby, a student from 1841-1844 and honorary degree recipient in 1885, was appointed Minister to China by President Grover Cleveland in 1885. He served until 1898 and is one of the longest serving U.S. envoys to China since the first U.S. envoy was appointed in 1843. Denby was an influential arbiter between China and Japan during the Sino-Japanese War in 1895.
In 1979 Georgetown's American Language Institute hosted 26 exchange students from the People's Republic of China for intensive English language courses. The courses were intended to enable the students to go on to conduct independent research at various institutions in the U.S. The Georgetown contingent of students was part of a larger group of over 500 Chinese professionals and scholars, in the fields of science, medicine and engineering. They were the first such group to visit the U.S. following the establishment of the People's Republic of China.
No. Georgetown, founded in 1789, is the oldest Catholic university in the United States. Saint Thomas University in Bogotá, Colombia was founded in 1580, and is likely the oldest Catholic university still in operation in America.