How do I test if my MySQL update query was successful in CodeIgniter?

As commented, have you tried $this->db->affected_rows()?

That will tell you how many rows were updated.

if ($this->db->affected_rows() > 0)
{
  return TRUE;
}
else
{
  return FALSE;
}

or

if ($this->db->affected_rows() > 0)
  return TRUE;
else
  return FALSE;

or

return ($this->db->affected_rows() > 0) ? TRUE : FALSE; 

EDIT

also(much better)

return ($this->db->affected_rows() > 0);