Yes, you can just copy the folder but need to get a registry key over to your desktop pc as well.
Have you ever done something like this? I will try to describe it as good as I can.
First click "Start" and then "run", type "regedit" into the new box and press ok.
The registry editor will now open and you need to go to the path "HKEY_LOCAL_MACHINE\SOFTWARE\Codemasters". In there should be "Operation Flashpoint" and "Flashpoint Resistance" (if you got both) or maybe something along the lines of "OFP GOTY".
Right-click on the Codemasters folder an choose export. Name the file and save it where you like, then copy it over to your desktop.
If you installed the game in another folder or hard disk you will need to edit the file, right-click it and choose "Edit" or open it with a text editor. There should be a line saying "MAIN"="D:\\OperationFlashpoint". This is mine, it should be the folder you installed it on your laptop. Change this to the one on your desktop if it differs and mind the double \\ between folders.
Now execute the reg file, it will ask you if you want to add the information to the registry. Confirm this and you should be ready to go.
One last note: If you have got Resistance or the GOTY edition including it you should patch to the latest version (v1.96) if you haven't already, as the CD check has been removed in the later patches. If you haven't got it yet I recommend it
If you have only got OFP:CWR you could try the CD first, it might start with it even if it won't install.