I very much doubt that a USB monitor will display anything during OS boot, and I'm certain it will not during earlier parts of the boot process (when the BIOS is in control).
From the prices I have seen the price difference between a USB monitor and a DVI or VGA monitor is much larger than a cheap graphics card would cost (larger still if you consider 2nd hand cards) so unless you need a USB monitor specifically for other reasons (yur main PC has no more unused VGA/DVI outputs, or you specificity want one of the small monitors not a full size one) you would be better of getting a DVI/VGA monitor and a cheap graphics card for the currently headless server.
Also, if the old machine is very old and so only has USB 1.1 ports you may have trouble as all the USB run monitors I've seen specify requiring USB 2.