You can have the term input empty, e.g.
if( has_term( '', 'genre' ) ) {
// do something
}
to see if the current post object has any terms in the genre taxonomy.
It uses is_object_in_term()
where:
The given terms are checked against the object’s terms’ term_ids,
names and slugs. Terms given as integers will only be checked against
the object’s terms’ term_ids. If no terms are given, determines if
object is associated with any terms in the given taxonomy.