If you're using air for just working mass and not for an oxidizer, it's my belief that this does not improve specific impulse but only improves peak thrust/engine weight.
Because the energy lost to the movement of the propellant goes up as the square of the velocity but the thrust goes up linearly. Bulking out your propellant by a factor of ten while reducing the exhaust velocity by a factor of ten doesn't change the resulting thrust, but reduces the energy you need for that thrust by a factor of 10.
