No. A separation agreement is essentially a legal contract, like any other type that involves two parties who agree on their respective obligations to each other. Provided that it has been entered into properly, with due regard to certain formalities (such as being witnessed), it is legally binding on you and your ex even if it has not been filed with the Ontario court.
With that said, a separation agreement can be filed if you want it to become part of your formal Divorce Order. In that situation, the agreement becomes part of the terms of that Order. In the event that your ex breaches its terms, his or her compliance can be enforced through the usual remedies that can be obtained by a court.