Il'd say no, only because I actually know how to protect my computer, unlike a large % of computer owners.
Last year, I don't know how but a botnet got on my computer, and because of my firewall I was monitoring everything it was doing, and it kept trying to open connections to one I.P and the firewall kept on blocking it every time, and by looking at the time patterns it looked like it wasn't connecting automatically, it looked like the "bot master" kept on manually trying to make my computer connect to his.
I looked up his I.P and reported it to his ISP, but I am not sure if anything happened.