The Friends Ambulance Unit was set up by Quakers during WW1 and its personnel records are now searchable online, with images free to view. Google fau quakers and you should get there.
The American Field Service was the U.S. version - mostly volunteer college students. They called themselves "Friends of France," but had no affiliation with the Quakers. Code: http://net.lib.byu.edu/estu/wwi/memoir/AFShist/AFSTC.htm Appendix G on the above page has an alphabetical roster. My grandfather is listed. He served 7 months before joining the U.S. army when we finally got in the war. -Barb