Would it have enough bandwidth? High speed connections have some careful engineering (for instance, maximum distance without a twist on a differential pair), that I doubt that ancient box has.

Also, there are sequencing requirements. Look carefully at a USB-A plug, and you'll see that the power and ground traces are longer than the data traces: when plugging the USB cable, the power is connected first, before the data; when unplugging, the order is reversed. HDMI probably has similar requirements, perhaps with more steps. Again, I doubt that ancient box can do that.