Yes, if you look at the $g_{rr}$ term of the [interior Schwarzschild metric](http://relativity.yukterez.net/05.html#1) 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 proper radius $R$ is larger by $\rm +1.5 \ mm$ than the coordinate radius $r$, and the proper volume by $\rm +4.5e11 \ m^3$ compared to the euclidean sphere. For a neutron star it depends on its specific radius and also the spin, which makes the metric different than Schwarzschild.