I don't quite understand the point of this?
A checkbox is a single-value input. It's either on or off. That's it. If the user selects a checkbox, you notice this after submission, and do what you have to.
I can't think of a single 'real life' scenario where this would be useful. Hidden fields exist for a good reason, and is most likely the best solution to your problem.
Please let us (me?) know what you are trying to achieve, and I'll try to understand 🙂