I think that the only thing that could happen are things on your screen only since all other guys must have some extra soft installed to get some sort of input from your shooting.
Being not multiplayer ready currently, the Weapons therefore can't trigger actions on other PCs.
Even if they get multiplayer ready later, this module (or whatever one likes to call it) has to be installed and active to trigger actions then.
I also doubt that Vatsim controllers will let you fly in a somehow attacking way to get closer to your targets. At least, the normal flight routes (no military areas) will stay like this for good reason.

So the only thing imaginable for now would be a somehow damaged plane showing up on your screen while the corresponding Vatsim buddy won't get harmed and continues to fly unimpressed on his system. I haven't tried so far though.