Honestly, I think your POD is going beyond implausible to highly-ASB. And I am not even sure the most determined Alien Space Bat can get the Romans to do what you are proposing.
Which Greek city had an elected assembly? The idea of representative democracy did not yet exist anywhere in the world and I am not sure anyone in the 1st Century B.C. would have come up with such an idea.
While I could see some support for a broad based public education system in Rome, I don't think the Senate would agree to it. Their argument would either be that anyone with any business in government is already educated enough for government or that it would be a tremendous waste of money for someone to need schooling just to be shepherded to the assembly and be told by his patron or the guy who was paying him how to vote.
And then there is the whole "citizenship" thing. By that I mean, who would get the vote. A generation before Octavian, a consul was murdered and a civil war (the Social War) was fought over the issues of giving Italians the right to vote in Rome. In other words, Rome was not quite set on the idea of allowing the handful of Italians with the time and money to travel to Rome the right vote. I cannot imagine the Roman establishment simply deciding to throw power form the nobiles and the rest of the senatorial class to anyone with a vote. One of two utterly impalatable things would have to occur. Either the urban masses would recieve control of the votes through sheer numbers and eager politicians would play the mob to gain power or large blocks of citizens would need to be stripped of suffrage so only the "right" people can vote. While I could see the Roman Mob not noticing that they had lost their votes (they didn't seem to care OTL when Tiberius abolished the assemblies), but they would notice if no one needed them to show popularity.