Maybe this has been stated before, but just because you are investigating a noise that you KNOW is nothing to worry about, while noting that most people would not carry a weapon to investigate the noise, I don't see a problem in choosing to bring a weapon. If you just HAVE to investigate, if you have a pistol and it's nothing, then you're fine, and the pistol wasn't a problem. But if Jack Nicholson's character from The Shining jumps out with an axe (
), then you're adequately prepared to defend yourself. However, if he jumps out when you don't have a weapon, you're worse off. What I'm trying to say is that there is no problem in carrying a weapon where you don't need one.
Whether you ARE clearing your house or NOT, being armed is a benefit. Unless the BG somehow wrestles it from you, I guess, but if that is a possibility for you, then you probably have no business clearing your house (I admittedly fall into this category).
Also, I'm guessing this intruder has a reason for being in your house. Most likely, he's there to steal something. His objective is theft, and your objective is clearing your house. You only have to be quiet enough so that the BG (who is either grabbing stuff or searching for stuff to grab) cannot hear you. If you are quiet enough, he won't know where you are, and he will be preoccupied with his theft. This gives you the familiarity with your surroundings and the element of surprise. The rest of this paragraph is meaningless, however, if he is there to harm you, in which case, you'll probably know before you get out of your bedroom if he's a professional.
As a disclaimer, this post was made without the benefit of professional training or personal experience. Please correct any fallacies, as this entire post was my imaginings of theoretical scenarios.