This sounds like two questions rather than one.
I feel like the real question is whether you can run VyOS on bare metal, and the answer is yes, you can. If you already have another Linux distro installed on that box, it should run VyOS just fine too.
Boot it from the VyOS livecd (or make a liveusb from it), login with “vyos/vyos”, run the “install image” command and reboot. The installer will reformat the drive though so make sure you save everything valuable from the old Linux installation.
If the issue is that you cannot boot that box from a livecd/liveusb, then there are two options. If the box has a removable drive, you can connect the drive to another (possibly virtual) machine, install VyOS on it, and put it back in that box. You may want to boot the temporary machine from the drive and adjust the config of course, e.g. serial console or network settings.
If the box has the flash soldered to the board, it’s more complicated, but still doable. You can make an image of a drive with installed VyOS, boot the box from USB or network, and dd the image to its flash drive. I’ve done that with my netgate box.
The answer to the first question, taken literally is “it’s complicated”. We build a number of packages that are also present in Debian apart from adding new ones, so it’s more a debian-based distro than a debian-based appliance. Our image build procedure now uses standard Jessie repos together with our own though, so technically if you put enough effort into it, you can turn a Debian Jessie into something that will look a lot like VyOS. The main issue is our binary install and image upgrade system. I think we have already removed the last bits of support for legacy non-image installations, so upgrading such a makeshift VyOS may prove very hard.