Depends on “how” the shoe makes you run faster if it’s by improving the grip and gate then yes it can make you fitter or at least reduce the chance of injury.

People that run in shoes not fit for running or in wore down shoes put their health at risk as well as making it a hell of a lot harder for themselves.

Also there is a psychological factor if you feel that you are improving you might be more likely to keep running instead of giving up.