No, on the database itself. I used "child side" for lack of better terminology. Every foreign key has two edges: the "parent" table and the "child" table. Rows in the "child" table depend on existence of matching rows in the "parent" table.
It should be feasible to run `gh-ost` to ALTER a table that only has "child"-side constraints. It will be impossible to run `gh-ost` to ALTER a table that has "parent" side constraints.
Hope this clarifies.