I agree with Shrink, I think it does make a difference, certainly for an espresso or ristretto. Or, stated more accurately, I can readily taste the difference, on my machine, holding all other parameters constant. Whether it matters is a different question.
I have made so many shots with my (now retired, a few days ago) machine + grinder that I no longer needed to weigh or dose. One day last summer (I was bored) I sat and made a few dozen shots in a row, eyeballing it and then weighing, and I was amazed at the consistency of the weight. I think you can do that if you make lots of shots, holding everything consistent, and if the environment is not too variable (where I live, it is just always dry).
Now, with my new machine, I am having to re-learn everything and I am weighing every shot, even when it is dosed at a certain amount by the Mazzer.
Always something to learn.