I don't believe you can download directly to the PCIII unless it is on the bike with the ignition on, but I think they sell an adaptor for direct loading to the PCIII. As far as laptop or desktop it dosen't matter.
Laptop is good for the running their program and actually watching the screen while you have the bike running at different rpms. They provide a nine volt adaptor so that you can download a map to the power commander unit from your desktop pc.
So, you can download from you desktop pc then take the power commander unit and hook it up to your bike.
Or, you can use a laptop connected to the power commander that is on your bike.