The simple answer is yes. I've compared badly aligned sensor board with a good aligned sensor board and I can tell the difference on the track in 17.5T motors. Can't speak on other motors, or on a dyno. I did keep everything the same in my testing, even the amp draw on the motor.

With this said, I think that the affect of having a bad sensor could be overcome by writing smarter ESC software that adjusts the timing of the pulse between the poles. I'm not sure how the software is currently handling the amount of time between reading the hall sensors and when they actually pulse the poll with voltage. So maybe some ESC just keep the time equal between all three phases and others might be smarter about how they handle it.

Unfortunately this is illegal

You think?
As long you will not have any influence on the timing and the ESC is determing the same timing every time you switch it on and give throttle you will have the ideal stock ESC

Yes. ROAR requires the phase change to occur within a set time after the motor signal changes in blinky mode. They're not allowed to do any fancy interpolation.

So an electronic timing through blinky is mandatory but the mechanical timing through the endbell is still endless.......

Over here we drive with a stock ESC with blinky AND a fixed endbell, so you have to have luck with positive tolerances. To outrule the (cheated) tolerances such an ESC would outrule it all.