Your system runs fast if it's got a lot of resources that it can use. It slows down when the system tries to use more resources than what's available.
So, for example, if you use up all your RAM with antivirus scanning - then your RAM usage in the game will be affected.
The problem here is that there are many "resources" in your computer and you can't always know what's consuming what resource. The most common resources are CPU, RAM, hard drive access, and video - but there's plenty more that will affect your system's speed.
I routinely run my anti-virus, have IE open with 8 tabs, and 2 instances of Firefox open with 10 and 22 tabs while I game. But I've got a boatload of RAM, so the performance hit is minimal.