Dr. Draper was an Assistant Surgeon General and later Deputy Surgeon General of the United States Public Health Service. After graduating from Harvard Medical School in 1910, Draper entered the Public Health Service, completing a two-year tour on the west coast followed by assignments near Washington D.C. During World War I he was commissioned by the U. S. Army as a sanitation officer, working at Camp Lee and Newport News, both in Virginia, and then conducting relief activities during influenza outbreaks in New England and Pennsylvania. Dr. Draper returned to the Public Health Service in 1919, and in 1922 was promoted to Assistant Surgeon General ahead of his peers. When the Virginia State Commissioner of Health died in 1931, the state's governor borrowed Dr. Draper to fill the position, which he did for three years. Five years after once again returning to the Public Health Service, in 1939, Draper was appointed as the Deputy Surgeon General, which position he held until his retirement.

During World War II, Draper was brought into the United States Army with the rank of brigadier general, and served in Europe under General Dwight D. Eisenhower as a member of the Civil Affairs Branch of the Supreme Headquarters Allied Expeditionary Force (SHAEF). Put in charge of the Public Health division, he was quickly promoted to major general, and received recognition for his work with the vexing public health issues created by the war, and their impact on the ability of the Allies to fight. Dr. Draper returned to the Public Health Service after the war, and retired from that organization in 1947.

Shortly after his retirement he became the assistant vice president for health services for the American Red Cross, but in 1948 was named the executive medical officer for the United Mine Workers (UMW) Welfare and Retirement Fund. Under his supervision, the fund created ten union-operated hospitals in coal mining regions of Kentucky, Virginia, and West Virginia. His two-decade tenure with this program brought him recognition and awards from the medical community. He retired from this position with the UMW in September 1969, but continued with the union as the special assistant in the newly formed UMW Department of Occupational Health until his death in 1970.

Doctor Draper was influential in many professional organizations and was the president of several of them. He lectured at a number of medical schools, authored 61 articles on public health and preventive medicine, and co-authored several books and pamphlets. His humanity, humor, compassion and warmth of character are evident in many of his writings, and in the words of those who knew him.