Does my Feature module have to explicitly define the body field in it's components?
... I always do. :)  It should be no problem -- and if for some reason the field doesn't exist on the destination server it will then be created (the Minimal install profile for instance I don't think has the body field by default). If you look in /profiles/standard/standard.install you'll see it creates the fields and basic content types in code, eg:

// Around line 229 of standard.install where $type is
// essentially 'page' or 'article'.
node_add_body_field($type);