Depends on the game. The large majority support 480P via component. Some do 720p/1080i, but it is a much smaller selection
I've got an X2VGA that I still play my Original Xbox With, I've always wondered how they did that, is it just an integrated Component->VGA adapter?
Can confirm that VGA output needs a BIOS mod - otherwise the picture will have a strong green tint. So yeah, those converters would have to be using the component signal. If you eventually decide to go the VGA route, keep in mind it doesn't work with (at least) the 1.6 boxen (unsupported encoder chip, or sth like that, iirc).
I have 1.1 and used the very early model of VGAbox from its creator. worked like charm although I sold the adapter box to someone from this forum many years ago. from memory it was YUV->VGA converter in a box. and think it worked with stock standard Xbox console.