Not really, the societies are too different to draw such conclusions. In less gender egalitarian societies a women without income is at the mercy of a sexist society. In more gender egalitarian societies, there is more social support and safety for women at lower economic levels. So in these less gender egalitarian societies, the drive to secure income is much greater and thus you would expect women to take lucrative but otherwise unappealing jobs. In societies where these pressures don't exist you would expect women to be less attracted to income in career choice. And this is how it plays out.
Yes, this is exactly how it plays out. This isn't proof, in itself, but it does seem to have predictive power as a theory:
"Galpin investigated the percent of women in computer classes all around the world. Her number of 26% for the US is slightly higher than I usually hear, probably because it’s older (the percent women in computing has actually gone down over time!). The least sexist countries I can think of – Sweden, New Zealand, Canada, etc – all have somewhere around the same number (30%, 20%, and 24%, respectively). The most sexist countries do extremely well on this metric! The highest numbers on the chart are all from non-Western, non-First-World countries that do middling-to-poor on the Gender Development Index: Thailand with 55%, Guyana with 54%, Malaysia with 51%, Iran with 41%, Zimbabwe with 41%, and Mexico with 39%. Needless to say, Zimbabwe is not exactly famous for its deep commitment to gender equality."
It's the same concept as FU money. In societies with poor gender equality, having financial independence is a crucial and powerful defense against societal injustice.