Well, you need either Windows or some kind of DOS to flash the card, too. Both need the EFI BIOS emulation module/driver in order to boot. However, as far as I'm aware, the original firmware of the 2006 Mac Pro (which works fine with the flashed card, by the way) doesn't have that emulation code. That means unless you have applied the firmware update that came with Bootcamp at some point, you won't be able to boot into DOS. I have no idea if this update has ever been made available via Software Update. In other words, a stock 2006 Mac Pro without the Bootcamp firmware update can't boot anything other than OS X (for all practical intents and purposes, that is).
Edit: Assuming you tried to boot from a FreeDOS CD, and it didn't work: You do not need a full-blown Bootcamp/Windows setup. You don't even need to run the Bootcamp wizard (however, a small FAT32 volume on the internal hard disk comes in handy in the process). All you need to do is install the Bootcamp package, which should install the firmware update during the next reboot. If you decide you do want to backup your original (4870) ROM, which is highly recommended (I'd have a fancy paperweight by now otherwise), you still don't need Windows - FreeDOS will do. In that case, run the Bootcamp wizard, let is shrink your hard disk by a couple of MBs, and simply don't insert a Windows CD when prompted to do so.