I'm not sure if I understand what your experiment consists of. Do you want to check if it's possible to learn a language by learning female forms first? You don't need a special course to do that, simply ignore the male forms as they appear and only pay attention to the female forms. Or do you want to know if it's possible to construct such a course? There is no reason for it not to be possible, but at least for Russian, it would require a lot of attention to how you construct the dialogues, so I don't think that such a course exists.
Russian verbs have different first person form in the past tense, depending on your sex. For example, when you want to say “I wrote”, as a woman you say “Я написала” and as a man you say “Я написал”. Similarly for adjectives: “I'm happy” for a woman is “Я счастли́вая” and for a man is “Я счастли́вый”. So such a course would have to make sure that no male in the dialogues introduces new gender-specific forms, new adjectives are introduced in example sentences about feminine nouns, etc.
For the same reason I don't think any Russian course manages to consistently introduce male forms first, unless it's very short. To check that, I googled "Russian course" and looked at the first result. In the past tense lesson you have "пошла", "спросила", "ела", "жила", "позвонила", "окончила", "начала", "посетила", all introduced for the first time in their feminine form, and not the masculine.
So I doubt that anybody cares enough to make sure that all dialogues and examples always introduce the form for one of the sexes first and the other sex later. I think the most likely person to care would be Suzette Haden Elgin, the constructor of the feminist conlang Láadan. But the Láadan course defines the third-person pronoun as “he, she, it”, so it looks like she doesn't care either.