VirtualBox USB Storage – Installing and Booting an OS from USB Drive

Is it possible to install an operating system onto a USB drive, and then boot to it, all within VirtualBox? Not like putting the virtual disk on the USB drive. Installing the entire OS there so it can be booted to from other computers as well. To be specific, the OS I'm planning on installing is Arch.

Edit, for clarity:

I have a Mac as the host. And I plan to use Arch as somewhat of a temporary host. I plan to run the LiveCD in VirtualBox and then install Arch not to a VirtualBox virtual drive, but to a USB drive that I can then boot other computers off of. VirtualBox will be simply a way to run the LiveCD. After this, I will want to do some configuring/testing on VirtualBox, with that USB drive. Will I be able to boot from the USB drive, almost as if it were a LiveCD?

Note that I also want this disk to be perfectly bootable from another machine, like a LiveUSB distro.