No, it will pass all the form data, whatever it is. The right way to do this is not to set the checkbox via a hidden field but to set the checkbox with whatever its state actually is!
I mean... why are you adding the hidden field to begin with?
Your PHP is receiving two fields named check_box_1, and last time I checked there was no way to guarantee that the params would get read into the REQUEST hash in the exact same order as you sent them, so, there's no way to tell which one will arrive last (that's the one whose value will get set). So... this is not the right approach to whatever problem you're trying to solve here.
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