No, the aphorism "behind every great man is an even greater woman" does not apply to Holden because he is not a great man. Even more, Holden mentions a connection with four females in the entire book—his mother, Sally Hayes and Jane Gallagher, and his sister Phoebe—and finds ways to destroy each relationship.
We can look at this aphorism and say that the opposite could be true: Holden is struggling in life because of his complete refusal to accept the love of any of the females in his life. As he's packing to leave Pencey, Holden becomes sad when he sees his skates because he imagines the love his mother put into purchasing them. He never truly pursues a relationship with Jane. He rejects Sally's efforts to bring him into her home. He smothers Phoebe.
While Holden is a character many people can relate to, his mental disorder keeps him from getting close to the females who love him, which prevents him from becoming a "great man."