Any software on your machine that can access the internet has the potential to give away your information. It doesn't matter if it's an antivirus, a game, or even a professional application suite.
AFAIK Windows doesn't have anything like AppArmor that would say "This program can do A, B, and C; but if it tries to do anything else it will be blocked." So there's nothing stopping a rogue program from doing bad things.
This is why something like Tails is very good for anonymity if you are not allowed to install a more secure OS on your machine. It may be a little slower and you might want to buy a fast USB stick but you can much more peace of mind when you need to be anonymous.