I searched for but couldn't find any documentation about how/if a .prj file is created when writing to Shape. From mapping file translations, sometimes this projection file is created alongside the core shapefile components and sometimes not.
Next week I am going to test a hunch that setting the COORDINATE_SYSTEM directive (or equivalent workbench parameter) for the writer allows FME to output a .prj file, while having it not set results in no projection file.