That is NOT an argument against the possibility that there is no "free will".
Let's look at it from the opposing side (the side that hears about the science showing intent may precede consciousness of intent in the brain): the hypothesis on this forum is that in that scenario the brain is really just an "AI" that has seen a lifetime-long "training set" of responses. The brain develops a suite of re-actions to any given stimulus which it zeroes in and and puts into your conscious thought as a "desire" or, if you will, an "impulse". The RESISTANCE of said impulse may be nothing more than another circuit activating that urges caution.
The really rough part of all of this is that you are INSIDE the machine...you ARE the machine. Is there a separable component that is your "essence" (aka "soul", "driver", "self") or is it all a function of a physical brain?
I have, in my life, seen many instances of the physical brain being broken or harmed and the resulting "self" that was coming out of that "brokenness" was unlike that person normally was. I have also NEVER seen a disembodied "soul" but I KNOW with 100% accuracy that without a physical brain no personality develops, and likely no life is even possible.
So, if the science seems to be giving hints that "free will" may be in question, AND there's no reason to believe in a person's essence separable from the physical brain, it kinda looks more like we are just animated meatbags who function on a quotidian basis according to what our neural network picked up from a lifetime of training.
I'll be honest and say that I'm not really happy with that explanation but if I'm also being honest about my "approach to knowledge" I would have to say that I can see some reason to believe it.