Yes, very much so.

Why?

I work with a fellow who won the Australian Iron Man some years ago and still regularly wins Master's races.

His son, a National Junior Champion, trains with the Olympic team and rides a fixed gear bike over the winter as a training bike.

They both have ridiculously low body fat and cannot take off any more body weight and still maintain normal health.
For that reason, they ride very light bikes.
As light as the rules allow.
For them, one pound on the bike equals seven pounds on their body.

My elder son, on the other hand, runs the 440 in college and has an exceedingly muscular body, and, in fact, an overly-muscular body for a bicyclist.
He has no interest in losing weight and rides a bike to cross train for running and other activities.
He couldn't care less about how much his bike weighs, as long as it doesn't break.
For him, an extra pound on the bike means nothing.

For myself, I have fairly light bike.
I have light components on a relatively heavy Pista frame, and it all adds up to a light bike for a street fixie.
I feel the greatest benefit in the low inertia wheels, and then again when I pick it up to carry it.
Otherwise, for me, fit matters more than weight.