No! To have proof that the Province of Ontario has registered your marriage, you need to purchase a marriage certificate. You can order a marriage certificate about 6-8 weeks after your wedding date.
A Marriage Certificate is the legal record of your marriage. It lists the date and place of the marriage, and names of the people who were married.
At your marriage ceremony, you will be given the Record of Solemnization of Marriage from the Officiant. It is considered a souvenir document and not a legal record. The official who performed your marriage is required to forward the Marriage Licence you signed on your wedding day to the Office of the Registrar General for registration.