Will a row update check all child tables which have foreign key relationships in InnoDB?
ON DELETE CASCADE: When you delete rows in the master table referenced by other tables, all those child tables will also delete their rows that reference the deleted master data.  
ON UPDATE NO ACTION: If you try to update a field in the master table referenced by others, MySQL will prevent you from doing that. NO ACTION and RESTRICT are synonyms in MySQL.


So to answer your updated question, MySQL will prevent you from updating a field in the master table that is referenced by any child tables because you specified NO ACTION.  If you are updating any other field in the master table it will take the same amount of time as an update on a table without foreign keys.