Just a reminder, because especially when you just started playing pool - this can have a big influence. I've switched my eye alignment after already playing for a couple of years, and it wasn't easy.
Your personal right cue alignment is most important for straight shots. It decides if a shot just looks straight to you, or if it is really straight. With the wrong alignment, the two 2D images that your brain receives by your eyes will be shifted, therefore a slight angle will look straight to you.
On angled shots it's not that big of a deal. You don't really see the aiming line from behind. The way it has to look to you has to be learned anyways. However, it can be the reason why you prefer a certain cutting direction (to the left or right) and have a higher success rate.
Your cue doesn't necessarily have to be exactly under your dominant eye. There are more factors that determine the right position, e.g eyesight of each eye, the tilt of your head, or simply if there are any anomalies of how exactly your brain is putting the images together.
The best example for that is Niels Feijen. He has only around 5% eyesight on one eye, that's why his cue is shifted over that much:
But this image of Ronnie O Sullivan also shows the different factors very well:
