CB has no hidden fieldtype. I suppose you could try adding one using a delimiter field and simply putting the HTML as the delimiter fields contents. However populating it is a different thing entirely.

For that you could use CB Auto Actions with a code action of JS or jQuery mode, which will append your supplied JS/jQuery to the header of the page (use before registration form display trigger). That JS/jQuery could check the select field and populate the hidden field based off value. However, this is purely JS based and there's no PHP validation to enforce it of course.

Is there a reason you need to duplicate a hidden field in this manner? Surely there's other better solutions, but will need more understand of what you're trying to do with it.

I recommend simply editing your plugin and extending it to supply what you need instead of depending on a hidden field. As for example I could use Firebug to alter your hidden field to whatever I liked without any sort of PHP side protection.