For example, is the phrase "Stars, to a good approximation, are spherical." correct and idiomatic English?
That is correct, idiomatic English, but depending on the exact meaning, you may be looking for "to a first approximation", meaning:
a roughly approximate value of a quantity often preliminary to more precise determination
The difference is nuanced, but my impression is that "to a good approximation" refers to a somewhat more exact approximation than "to a first approximation" (in that one could make better approximations after the first).
Google Ngrams Viewer suggests that both are used in writing, with "to a first approximation" being somewhat more common. Also, both are declining in usage in modern writing.