No.
First, you have the contract, recognised by the state, with legal consequences adhered to it by law. No religion should influence law making and religion has nothing to do with the marriage "before the law".
You can add whatever religeous ritual to your marriage, if you want to, and call that ritual "marriage" as well, but that's your religious marriage, taking place in the private sphere where you can do whatever you want. It is not (or should not) be equal to the marriage before the law. Your religeous ritual called "marriage" is not the same as the marriage before the law, which has legal consequences.
At least, that's how it should be. Belgium has it right: a) you marry "before the law", an officer of the state (usually the mayor of your residence) takes note and that's it ; b) after your "legal marriage", you can go to church and marry again, for a priest (or you can perform whatever ritual you want or no ritual whatsoever) which has no legal consequences
Strict separation between church and state, as it should be in any modern, civilised society.

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