I would say, "DO NOT DO IT!"
I mean, if it is for upgrading your old desktop in order to have a "nice running desktop PC" then you should of course do what you explained. It is a very good choice.
If however, it is for running CoD on your desktop, do not bother, it will be a waste of your time.
Your graphics card is just bad (for this game). It is like trying to drive a Ferrari on wooden tyres.
CoD's graphics were not done well (it is a common secret). They are either too complex for their time or, too poor programmed for performance (opinions vary).
You need a GPU with 1,5Gb VRAM and more in order bypass the first game bottleneck (VRAM usage) and fly well. The next game bottleneck is Dix10/Dix11 performance (and there is no GPU today with enough power, for CoD). Your GPU underperforms in both.
So you should probably be happy that you can enjoy CoD on your laptop and if you want to make some good investment you should probably by one laptop tray with fan in order to keep your laptop cool
My 2cents...