I use to have several Gamestudio versions on a USB drive, so I can confirm that it works. Of course, you need to make sure that you have full access rights to that drive on the PC you're working with. Also, registry dependent features such as opening a script or level with double clicking on a c or wmp file won't work with a USB drive.

The easiest way is installing Gamestudio on the PC, and then copying the whole folder to the USB stick.