I think you would have to take care of that beforehand.
But, you need both systems to transfer your data to a new 2DS/3DS and you move your data from one console to the other without losing your stuff. It's more of a "ID for a console" instead of "ID for a person" as you can't really have multiple consoles for one account, that means you would have to re-download/purchase everything, your games are attached to the console.