5770 cards require one 6-pin Aux power cable from the motherboard to the card. Aftermarket cards do not always include it, but it MUST be connected.
That is a PC-BIOS card flashed with Apple Firmware. In general, such cards do NOT show the Boot Screens or any diagnostic screens. The first screen you see will be the login screen, or if you auto-login, the desktop.
The seller says It will show the Boot Screens ONLY if you connect an Analog VGA display (with adapter) to the lower DVI-I port.
Drivers for accelerated operation of this card are included with custom 10.6.4 shipped with certain Mac Pros, and in standard 10.6.5 and later. All appropriate Drivers are already included in Mac OS X -- there is no need to install them later, and no way to do so since they will not work in older versions.
Official information lists the Mac OS X that shipped originally with your Mac Pro 1,1 as 10.4.7, but it may have been as late as 10.5. These are not likely to work with that card. You would probably need to purchase a 10.6 DVD from the Apple online store, about US$30.
Most Users who are not developers would be better served with a genuine Apple card, which would show a picture from power-on. But it costs close to US$250.