It’s all, cough, implementation dependent. You can run two VideoBIOS implementations, and chances are only one will install an int10h handler, but both will set up the registers and whatnot in the GPUs.

My AMD TAHITIs for instance need VideoBIOS to start some form of thermal management loop - otherwise they just run full-throttle on the fan.

Then whichever card prevails (BIOS has the ability to select the initialization order) becomes the boot display device.

X11 has some (generally working, for well behaved GPUs) emulation of this environment, so that the GPU can initialize late, and even reset under X control. This is how sane cards can work under headless ARM etc.

Now, some manufacturers assume you get something like SSE or MMX - VideoBIOS spec technically mandates 386 instruction set only. That crap gets badly emulated.

On top of this, drivers can sometimes reinit anyways, from native kernel code. If that happens, the VideoBIOS concerns are moot.