A good instrument makes a difference. It helps a student progress
faster and a good player sound better.

Some players sound better on electric or accoustic, finger-style or pickstyle. The style influences the choice of guitar and vice-versa.
Django Reinhardt's best work was on his choice, the Selmer accoustic Modele and when he played electric guitar, it didn't quite sound
like him.

I don't think that many classical guitarists would be able to sound
as good on an electric solid body.

Style is an indicator of how you will sound. In Chicago, I played Big Bill Broonzy's guitar and couldn't come close to making it
sound like it did when Bill played it. I heard him live many times, there. People have played my Martin 0021 and can't make it sound
like I do even though they were good players. I can't make my
style sound right on a dreadnaught or other types of Martins.
A lot is playing on what you are used to.

I think that accoustic-electric guitars that are run through a direct box sound synthetic and I think that it hurts good accoustic players to do that. They would be better off with a high quality condensor mic pointed directly at their instrument.

So....yes a better instrument affects that quality of your playing
and not everyone can equally sound good on every instrument.

Frank Hamilton