Can I use me laptop install disk with a purchased Key Code?

I have an older desktop that I want to upgrade to Win7 (Clean Install).

I also have a new Samsung laptop that came with a Win7 Home Premium 64bit SP1 install disk, which I used to do a clean system install on the laptop. I also have full C:Partition images to go back to at any time I need to.

Now, my question is this: If I purchase a license key, can I install Win 7 on my desktop system, using the disk that came with my laptop, and then activate it with the new license key?