The only downside is possible loss of operational security.
If you can come up with a way to live stream it without any of the text discussions being shown, or map indicating where the battle is occuring, have at it. Otherwise, not from my side please. If the opposition wants theirs shown, I'll be tuned in.
I am not sure, however, how someone who doesn't know the game will be exposed to the live stream. If they don't know enough about the game to actually play the thing, how will they know enough to find the link? I'm pondering this as well as it's not exactly a new thing to me, I've been live streaming for several years on classes and events. How would you get the viewers? I know what I have to do to get people interested. I use live streaming over the course of multiple subjects all geared to get them interested enough to sign up and attend the main event. I don't live stream the main event.
Have you considered building a viewer base by perhaps live streaming action from the Main Arena? You'd build an audience, and then that audience would be turned onto the scenario to actually play in it. If your intention is to attract new players to the game and events, then attracting them after the event starts is behind the curve. Start it now, practice now, build a base early, get them to fly the premium stuff. Marketing efforts
And, my opposition doesn't get to see my stuff!