Notice that Snowflake logic does not support the CHECK clause in the creation of foreign keys. The WITH CHECK statement is marked as not supported. Besides, the WITH NO CHECK clause is removed because it is the default behavior in Snowflake and the equivalence is the same.
Please, review the following examples to have a better understanding of the translation.
SQL Server
ALTER TABLE testTable
WITH CHECK ADD CONSTRAINT testFK1 FOREIGN KEY (table_id)
REFERENCES otherTable (Othertable_id);
ALTER TABLE testTable
WITH NOCHECK ADD CONSTRAINT testFK2 FOREIGN KEY (table_id)
REFERENCES otherTable (Othertable_id);