They will still pass juice, but they will pass it to the wrong page - namely the one with the affiliate id in it. And then, you might even get a situation where that page ends up ranking in the search engines over your own. The affiliate will certainly be happy with that of course, but you probably won't be
A workaround would be to 301 redirect the user as soon as you've recorded the affiliate and they've hit that page. It's slightly less valuable than a direct link to mysite.com/product-one but it's better than a link to the affiliate page.