Outside of possible scenarios involving whole-program optimization, the code code generated for something like:
struct foo *bar;
struct foo *test(struct foo *whatever, int blah)
{
return blah ? whatever: bar;
}
will be totally unaffected by what members struct foo might contain. Because make utilities will generally recompile any compilation unit in which the complete definition of a structure appears, even when such changes couldn't actually affect the code generated for them, it's common to omit complete structure definitions from compilation units that don't actually need them, and such omission is generally not worthy of a warning.
A compiler needs to have a complete structure or union definition to know how to handle declarations objects of the type with automatic or static duration, declarations of aggregates containing members of the type, or code which accesses members of the structure or union. If the compiler doesn't have the information needed to perform one of the above operations, it will have no choice but to squawk about it.
Incidentally, there's one more situation where the Standard would allow a compiler to require a complete union definition to be visible but would not require a diagnostic: if two structures start with a Common Initial Sequence, and a union type containing both is visible when the compiler is processing code that uses a pointer of one of the structure types to inspects a member of that Common Initial Sequence, the compiler is required to recognize that such code might be accessing the corresponding member of a structure of the other type. I don't know what compilers if any comply with the Standard when the complete union type is visible but not when it isn't [gcc is prone to generate non-conforming code in either case unless the -fno-strict-aliasing flag is used, in which case it will generate conforming code in both cases] but if one wants to write code that uses the CIS rule in such a fashion as to guarantee correct behavior on conforming compilers, one may need to ensure that complete union type definition is visible; failure to do so may result in a compiler silently generating bogus code.