Flavio bom dia, 
O erro persiste ?  Fiz alguns testes aqui, e mesmo se o retorno for vazio, o seu Toast seria criado, entretanto não mostrando nada !
Vi ali no erro que ele volta duas linhas dentro da sua AsyncTask, a linha 20 e a 41, você falar quais são esses erros ? 
Vou colocar aqui o código junto dos imports dessas minhas classes, tenta fazer o teste ai e vemos o que acontece !
package br.com.caelum.fj57design.servidor;
import java.io.IOException;
import java.io.PrintStream;
import java.net.HttpURLConnection;
import java.net.MalformedURLException;
import java.net.ProtocolException;
import java.net.URL;
import java.util.Scanner;
/**
 * Created by matheus on 10/09/15.
 */
public class WebClient {
    public String post(String json) {
        try {
            URL url = new URL("https://www.caelum.com.br/mobile");
            HttpURLConnection connection = (HttpURLConnection) url.openConnection();
            connection.setRequestMethod("POST");
            connection.setRequestProperty("Content-type", "application/json");
            connection.setRequestProperty("Accept", "application/json");
            connection.setDoOutput(true);
            PrintStream saida = new PrintStream(connection.getOutputStream());
            saida.println(json);
            connection.connect();
            String resposta = new Scanner(connection.getInputStream()).next();
            return resposta;
        } catch (MalformedURLException e) {
            e.printStackTrace();
        } catch (ProtocolException e) {
            e.printStackTrace();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return null;
    }
}
E agora :
package br.com.caelum.fj57design.asynctask;
import android.app.ProgressDialog;
import android.content.Context;
import android.os.AsyncTask;
import android.widget.Toast;
import java.util.List;
import br.com.caelum.fj57design.Dao.AlunoDao;
import br.com.caelum.fj57design.converter.AlunoConverter;
import br.com.caelum.fj57design.modelo.Aluno;
import br.com.caelum.fj57design.servidor.WebClient;
/**
 * Created by matheus on 10/09/15.
 */
public class EnviaDadosServidor extends AsyncTask<String, Void, String> {
    private Context context;
    private ProgressDialog progressDialog;
    public EnviaDadosServidor(Context context) {
        this.context = context;
    }
    @Override
    protected void onPreExecute() {
        super.onPreExecute();
        progressDialog = ProgressDialog.show(context, "Aguarde ...", "Enviando dados para o servidor", false, false);
    }
    @Override
    protected void onPostExecute(String media) {
        super.onPostExecute(media);
        progressDialog.dismiss();
        Toast.makeText(context, media, Toast.LENGTH_LONG).show();
    }
    @Override
    protected String doInBackground(String... params) {
        AlunoDao dao = new AlunoDao(context);
        List<Aluno> alunos = dao.pegaAlunos();
        dao.close();
        AlunoConverter converter = new AlunoConverter();
        String json = converter.toJson(alunos);
        WebClient webClient = new WebClient();
        String resposta = webClient.post(json);
        return resposta;
    }
}