(Everything ensuing refers only to the Roman upper aristocracy, i.e. senators, equites and their clans)

Remember the mos maiorum, the Roman code of what it meant to BE a good Roman and moreover, a good politician. Part of being a good Roman politician was an effective and illustrious military career, something a woman would be excluded from participating in at pretty much every level.

Also recall the concept of the paterfamilias, the title of a patriarch of a Roman clan. The emperor was considered paterfamilias of Rome, and patriarchy was ingrained in the Roman idea of what an Emperor was. So, in my opinion no, it was always impossible. Women held an important place in the establishing and maintaining political alliances through marriage, and in their own ways brokered power for centuries, but never via an official post or office.