Following graduation from New York's Brearly School, Greacen studied at the Grand Central Art School with Arthur Woelfe, Howard Hildebrandt, Guy Pene du Bois, Jerry Farnsworth, Wayman Adams, and her father, the head of the School, Edmund Greacen.
Greacen initially specialized in painting still lifes, but later turned to portraiture, and became especially known for her portraits of children. She taught painting and drawing at the Grand Central Art School from 1933 to 1943. In 1935 she became a member of the Grand Central Art Galleries, and in the same year married Ren‚ Bard Faure, business director of the Grand Central School. The Faures moved to Scarsdale, New York, in 1946, and from that time Greacen maintained her studio and taught in the Harwood Building in Scarsdale, and was active in Westchester County community life. In 1969 she moved to Florida.
Greacen's memberships include the Allied Artists of America, Audubon Artists, the Artists Professional League; and the National Association of Women Artists, of which she was at one time vice president. She exhibited with all these organizations, and received a number of their awards; she received a Hallgarten Prize in the Academy annual exhibition of 1936.