Is it permissible to pay $700 directly to the American agency to obtain another course without paying the $200 to the employer, knowing that the latter deducted this amount from the price of the first course?

It is not permissible to register for courses without the employer's permission, because this constitutes circumvention of his right to the registration fees agreed upon with the entity offering the courses. The fact that the contract did not stipulate your benefit from them does not permit you to circumvent it. The official steps must be followed. If the employer permits it and waives the fees, then there is no objection. Otherwise, it is not permissible, because Allah Almighty says: "O you who have believed, fulfill [all] contracts," and because the Prophet, peace and blessings be upon him, said: "Muslims are bound by their conditions."