I don't think so, since the next avatar will be born to Earth Kingdom he/she would already have learn earth bending. So maybe Mako could teach him Fire bending and Ikki, Meelo, or Jinora can teach them air bending
Everyone wants a Zuko/Katara hug in Korra." and as one of the commenters says: "We NEED a Zuko and Katara hug in Korra- they are the only memebrs of Team Avatar that are still alive!" I really believe that that has to count for something.