Wh1te Out: You shouldn't have a problem at all. Activation and updating can take place in any order. Activation is actually not required for the retail build (the version on the CDs), only for versions 1.1 and newer. If a game of v1.1 and newer is run, it will look for that sig.bin. Since you have it in your GalCiv2 directory, you will not be prompted to activate. If this is deleted or corrupted, that's when the activation dialog will come up again.
You could update if you'd like (there is a 1.3 Beta available*), though remember that at this point, you should not have to worry about activation again
*Beta updates are available through Stardock Central available here: https://www.stardock.com/sdnet_login.asp
Just log in with your nickname and password and you should be able to download Stardock Central. Once you have this up and running, you need only log in with your email address (gmail) and password, then any GalCiv2 updates will be available to you through the 'Games' section on the left. When new updates become available, Beta or otherwise, Stardock Central will notify you and prompt you to update. The process is streamlined, so this will make acquiring updates much easier.
Glad I could help!
-Mike
[Stardock Support]