Yes, most would consider pragmatic language deficits eligible under the speech/language/communication disorder category.
It sounds like a significant portion of your concern is not purely expressive language, but written expression, especially in extended, analytical/inferential writing. In that case, achievement testing that targets lengthier writing products might also be informative. E.g., the TOWL-4.
If his oral expressive skills are that high, then, yes, the CELF probably would not delineate his language skills very well. Another approach, which has less psychometric rigor, but more face validity for most classroom teachers, would be to use Six Traits Writing rubrics to pull out the elements of writing that he is most lacking.
http://educationnorthwest.org/traits/trait-definitions
