Ok.. so the preflashes still shoot before the shutter opens.
The question is does it affect the photo if it does. I think both happen simultaneously and it can register on the sensor. I do know that a shutter can open and be closing before a flash fires.
Here is how to find out. Take a flash photo in a totally dark room - light proof box or somewhere. (at the flash sync shutter speed or any slower speed will work) and rig the flash so it can't flash but the pre flash can. Did the pre flash register? I did and it did not register to the eye. The histogram shows nothing but that don't mean that the tiny amount was not there.
A person can do this no fuss.
Totally dark room with no windows - like my bathroom.
Camera in manual and bulb with rear curtain flash settings
Push shutter release and hold so that pre flash fires as shutter opens
Place lens cap on lens before releasing shutter and firing the flash. Done this way to prevent main flash from registering on the sensor.
Did the pre flash register? I did and mine is not detectable to the eye. Even so if it was there it would be insignificant in terms of exposing the photograph. it is like taking a photograph of a star at night using 1/1000 sec and F 8 - the star would not show up. But we know the star was there.
So the answer is no. The pre flash does not affect the photo.