The license key is per unique computer so the way you are "updating" will only use 1 instance of the key. Also the computer does remember the key so you should find that reinstalling will not require you to reenter your registration information.
There have been some issues updating from an old version using the automatic updater so in some cases a reinstall is necessary. Always make sure you have a database backup and a copy of the the themes directory if you've customised these.
Feel welcome to email us at email@example.com if you have any further questions about the process.