The baseboard takes the xbox vga rgb signals and extracts the composite sync from the green video signal.
It also converts that vga signal to a component signal that outputs on the middle unused connector. (seems to be a japanese standard for component.)
The only baseboard circuits that are powered by the avip cable 5V are those video processing circuits. The 2 microcontrollers that handle JVS and force feedback are powered separatly.
One issue you will have is the video cable detection on the main board. It uses 3 pins to detect the type of video cable connected. On a chihiro, it can be set with 3 dipswitches on the filter board and those are all 3 on. On a normal xbox, this is scart RGB 15khz. On a chihiro, it's vga.
So your component to hdmi likely will be detected as a component cable. it will expect component on the RGB outputs as well. No idea if the chihiro will be willing to produce a component video signal with the video cable detected as a component.
Most of the component to hdmi chipsets have a vga 2 hdmi option as well. (a pin of the chip that needs to be grounded or tied to vcc.
So, if the adapter is like that, it should work if the main board if all 3 cable detect inputs are tied to gnd and the chip is able to convert vga to hdmi.
Maybe it works straight away if the chihiro bios is outputting component. This still needs testing.
My point is that the base board works fine without the avip cable. (besides producing some video output)