Yes. This is correct. Holy mother Sarada Devi has a vision to establish a nunnery to uplift the women. She wanted that to be an completely independent organization managed by females without any male involvement from Ramakrishna Mission. This is known from the correspondence of Swami Saradananda with Mrs Ole Bull.
In fact Swami Vivekananda has also wanted to establish a nunnery in the name of Sarada Devi first before establishing Ramakrishna Mission. But he changed his decision on the advice of holy mother. She suggested, first establish a mission for men and then another for women later.
Today Buddhism and Christianity nunneries are managed by their male counterparts throughout the world. After seeing the example of Sarada mission’s good management skill, those nunneries are rebelling against to acquire independence in management.
Though west talks a lot on women rights, women freedom and feminism, still they are not liberal to give freedom to women organization. But India is far ahead on this front to establish an independent nunnery managed only by women