The external 20GB USB drive should work. However, I think you are asking if you can install a Linux distro in the drive and use it as a boot drive.
The answer to that depends on your PC BIOS, not Linux. Your BIOS must give you the option of booting a USB storage device. Plug in the USB device (do not use a USB hub). Power on your PC and go into the BIOS configuration (see your owners manual). Look for a section that describe the boot devices, and see if your USB device is listed as an option. If it is, you can use it as a boot device.
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