Well, hugging probably would have ended the outburst if only because John would be too busy flailing around and having a panic attack to have time to be upset about where he was.
...But the apology was still probably the better option.
While the apologies don't really calm him down, he is able to...attempt to calm himself somewhat, though his voice is still prone to hitching unfortunately high. "You're asking me to live a life without everything I love. Without teaching, without my home, without Joan? What sort of life is that? How can I live a life knowing she's out there and I'm here?" Of course, the historian in him was interested in the possibility of Reinette Poisson being somewhere on the ship, exactly as the Doctor intended, but his thoughts of Joan, and despair at the loss of everything else he'd come to define his life by, overwhelmed that interest for now. "I am me amongst a world created for you!"