I don't think there's a problem with it. I go to small but professional theaters and they often present plays that are not completely traditional, or are even experimental.* I went to a one-woman play one time where the character handed out food and drink to the audience (I got a cookie and a pat on the back . . . but I didn't get any coffee!). This wasn't just a student play, the actor at the time was head of the local Shakespeare Theater and has had small parts in movies.
If I recall correctly, what you describe has been done before, that is, the audience as jury, or citizen of Athens, or whatever. I think it's an intriguing idea as long as you do it well.
Good luck.
*One of the theaters tried putting on Waiting For Godot using women as the characters a few years ago. They advertised it heavily and were just ready to open . . . when the trustees of Beckett's estate said they couldn't substitute women for the male characters. Apparently Beckett was a stickler for doing his plays as written and the trustees thought they were following his wishes. They threatened legal action and the play was never put on.