Perhaps, but that is an extreme exception, so it follows that it has basically zero impact on why mosques are segregated.

In the early days of Islam, women were fairly independent. For example, the Prophet’s first wife was a prominent merchant and much wealthier than he was. One of his other wives, Aisha, was an extremely respected narrator of Hadith, even after his death.

Things changed slightly over time as: (1) local cultures mixed with the religion and (2) different branches of thought arose, each with their own interpretations and understanding of the religion. This, combined with the dominance of patriarchal societies in the region, led to women having fewer chances to participate in the workforce.