No - because they all have 15 pound bikes. But it does over a 19 pound bike.
For the regular rider, it does not matter. For the racer - some races it does.
Using your Velodrome example...
You can get that bike for $2000, $4000 and $6000. I don't see much difference. But the $900 bike - there is a difference.
At no point at the world class level is a difference of 4 pounds insignificant. And likely not 1 pound. But, a moot point as that doesn't happen.

So the boys did national team pursuit last year - Carson velodrome. We had one rider that was a regular track rider. He had the nice stuff. The other guys didn't have that level stuff. The difference between the road equipment and those same riders and the velodrome equipment mattered. It mattered because winning is such a small margin.