Kingdom Hearts II Does Roxas have a heart?

i think he has a link to sora's heart so he feel emotions that may not be his.

 

So he seems to have a heart because he seems to show real emotions...

My theory is that nobodies all have hearts, lost far away inside themselves, and some of them, like Roxas and Axel, were discovering that they did have a heart. But nobodies like Xehanort dont realise that, and make very heartless actions, and would never discover that they have hearts.
Roxas' actions may have been unlocking his heart, and releasing it from the nothingness inside him, and the same thing for Axel.