A huge part of the Roman political / cultural mindset was that a Citizen of Rome must be able to serve in the army to prove that they were qualified to serve the Roman state as political leaders.
This is correct for a patriarchal society. In a more emancipated or even slightly matriarchal society (mater familias instead of pater familias) the roman rule, that the comitia are more or less representing the army would not develop. The matriarchs would prevent such a constitution from the beginning.
Men would still focus on war, and there would perhaps be one assembly of male only for recruiting, preparing war, electing officers and generals and such. Probably still summoned and led by a female high-magistrate. But this would not be the highest and really important assembly.
Also in such a society, the magistrate would look fully different. You would see women as quaestors at least for the city, as praetors and aediles. And if you organize the consuls a bit different the one consul who stays in Rome and leads the sessions of the senate could be a women. The "imperium" as almost royal power always including military power, as the one and only foundation of government, would also not develop as it did. So you could end with a lot of women, if not a majority in the senate.
Very theoretical and fully ASB for ancient times. But the assumption, mentioned above more than once, that women have to participate in warfare by all means in order to rule the state is not mandatory. Not in the OPs theoretical and fully unroman construct.
I also doubt, that it is mandatory, that Rome never makes it beyond Latium with such a matriarchal system. Women in politics seem to be more rational and relaxed, but not less ambitious and cruel. Well, if the rest of the world is patriarchal, the resistance and hate against roman rule would be enormous. And this is why this little experiment would most probably fail in ancient times. If these matriarchs don't invent something even more clever than the roman socii-system.