I'm not sure that's entirely true as described. There's no reason why FlashBIOS would check for the hard drive or the DVD, and so long as you used the network to flash a hacked BIOS that bypassed the DVD check you should be fine. However, you would then need a hard drive to build a working Xbox, and unless you installed an X3 / Smartxx chip you would need a DVD drive to allow you to boot an installation disc and build your new hard drive. So, the short answer is you would need a DVD drive to complete the installation, and a hard drive to install the dashboard onto.
On second thoughts, that's also not entirely true. You could do the whole thing without a DVD drive, by flashing a DVD check bypass BIOS, then using xboxhdm to build the new hard drive.