I'm up for trying my hand at either a TA or professor. A professor would probably be preferred (assuming you think I'm up to par), because I work a ton of hours, and I'd rather the students have a TA who is able to more reliably be available at different points throughout the day to make sure they are able to communicate with their student enough.
Also, this has been done before (at least, it was in the planning stages, but I'm not sure if it was ever executed). If I recall correctly, the countries for the TAs were not publicly known to avoid any concerns of meta-gaming (not the cheating variety). Say, for example, I was the Italian TA, and Chaqa was the Austrian TA, if I knew that Chaqa never covered Trieste, it could influence the advice I give to my student, consciously or otherwise.
For the students, it could go either way. I'd learn toward making the game non-anon, because it's nice having a name to a country for the spectators. It's more fun cheering "YEA! GO NEWGUNBOATPLAYER2014!!" than simply "YEA! GO AUSTRIA!". Additionally, these will be students who will be receiving advice from their TAs. I don't think their prior tendencies will factor in too much, even if their opponents chose to go back and look at them.