First some terminology:
- Every OWL ontology is a set of OWL axioms.
- Every DL-Query is an OWL class expression.
- Every DL-Query result is a set of OWL entities.
You can only add axioms to an ontology. You cannot add class expressions nor sets of entities to an OWL ontology.
The "Add to ontology" button seems to create a new EquivalentClasses-axiom on the basis of the query (i.e. class expression), and a named class (given by the user), and then asserts this axiom into the active ontology, i.e.
EquivalentClasses(new_name query)
(I didn't quite get it working like this in my version of Protege 4, but such a functionality would make sense.)
The current OWL2 specification does not say anything about how to store class expressions and query results in the ontology. These have to be specified and calculated every time from scratch after you load the ontology from the file.