Click on your email address in the box next to Account: in the top right hand corner. Enter your password. This will take you to your account info page where it will tell you how many computers are authorized to play music purchased using your account.
To answer your real question, no... as long as you are using the same computer you can wipe and reinstall a million times and it will not mess up your authorization. You will need to enter your password the first time you play a purchased song after a wipe and reinstall but it will not increase the number of authorized computers. I believed the authorization is tied to your computer's serial number (someone want to verify this?).