How would they know if you were married and divorced?
I don't think they would but we didn't have a certified copy of her divorce papers so we couldn't get married in Belize. I guess if we had not brought it up, who would have known? Unless there is something in the Passport that would have revealed it.
You fill in a form and it asks you to reveal your history. If you sign and lie about it that is a criminal offense - and of course your new marriage would be invalid. And that might not matter right now, but it might cause problems down the road.