At the risk of penning the impopular answer, I am not entirely sure whether checking the return value of PDOStatement::execute() is a worthwhile endeavor when PDO::ERRMODE_EXCEPTION is in use, which it should. Or, to answer your question as you formulated it, PDOStatement::execute() returning FALSE indeed appears to be quite a theoretical scenario under PDO::ERRMODE_EXCEPTION — And if it indeed does happen, your request (if not the entire Apache process) is very likely doomed anyway.
The “genuine” occurrences of RETURN_FALSE in the source code of PDOStatement::execute are few and far between. By “genuine” I mean not commented out, and not following PDO_HANDLE_STMT_ERR (which is just pdo_handle_error, which does as it says in the name). In fact, it appears that the only cases where PDOStatement::execute could possibly return FALSE (again, under the assumption that PDO::ERRMODE_EXCEPTION is set) are memory alllocation errors, which are very likely to be unrecoverable.