Yes, if you look at the $g_{rr}$ term of the inner Schwarzschild metric for homogenous spheres you'll see that $\surd g_{rr}={\rm d}R/{\rm d}r>1$, so the proper volume (measured with stationary rulers) is larger than that of an euclidean sphere of the same cirumference.

For the [earth](https://i.imgur.com/u5AGCpV.png) the radius is larger by $\rm +1.5 \ mm$ and the volume by $\rm +4.5e11 \ m^3$ compared to the euclidean sphere. For a neuton star it depends on its specific radius and also the spin, which makes the metric different than Schwarzschild.