Transforming a crtieria to a SQL String (without parameter values) seems possible in order to implement CriteriaQueryImpl.toString(). See for example:
http://stackoverflow.com/questions/554481/how-to-get-sql-from-hibernate-criteria-api-not-for-logging

Otherwise transforming a criteria to a JPQL String seems also possible but probably requires more code.
For Query-AST as String, I don't know.