If you brine a chicken and then boil it in soup, how much salt, if any, will come out and go into the liquid?
I'm not exactly sure why you're trying to brine then boil; you should be able to simply boil your chicken in salty stock and get plenty of salt into it. It won't take nearly as long as brining, because things happen faster in boiling water.

Assuming you boil for any significant length of time, much of the salt will indeed come out into the cooking liquid, and you'll end up with your soup approximately as salty as the chicken. (If the chicken is in large pieces, this of course only applies to the part the brining and cooking liquids can actually reach.)