Hi, although I cannot give you a definite answer on this, I can inform you from my own experience.
I use MySQL and Apeache on a computer which is always on and connected to the Internet, and have never encountered any problem with it using much bandwidth.
Of course though it does depend on your Internet connection speed, and how much bandwidth you have actually got to play with. (I use a 2mbps connection which as I said seams to be perfectly adequate for the job.)
But from my experience, I don't really think it is any to worry about unless you have a very slow Internet connection.
I hope thats makes some sense and is of some use to you.