The VM is a container, a .pvm file. When you install the new version, it will delete the old version of PD and just use the same .pvm file(s) for your VM(s).
To answer the questions on "I already upgraded to Mavericks and now need to upgrade my Parallels Desktop 7 (or 8) to 9"
You can purchase an upgrade key via the Parallels Online Store -
Once you have your new product key, please visit http://www.parallels.com/products/desktop/download
On the page there is a link for "already have an activation key"> click this link
This will launch the .dmg files and walk you through the activation process with your new key.
Please note, you may need your PD7 activation key. This can be found in the My Account section of www.parallels.com