Will page build between push and pop?

main.dart

// Copyright (c) 2019, the Dart project authors.  Please see the AUTHORS file
// for details. All rights reserved. Use of this source code is governed by a
// BSD-style license that can be found in the LICENSE file.

import 'package:flutter/material.dart';

void main() => runApp(MyApp());

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      debugShowCheckedModeBanner: false,
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: MyHomePage(title: 'Flutter Demo Home Page'),
    );
  }
}

class MyHomePage extends StatefulWidget {
  MyHomePage({Key key, this.title}) : super(key: key);

  final String title;

  @override
  _MyHomePageState createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  int _counter = 0;

  void _incrementCounter() {
    setState(() {
      _counter++;
    });
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text(widget.title),
      ),
      body: Column(
        mainAxisAlignment: MainAxisAlignment.center,
        children: <Widget>[
          FlatButton(
            child: Text('Push to 1'),
            onPressed: () {
              Navigator.of(context).push(
                MaterialPageRoute(
                  builder: (_) => OtherPage(1),
                ),
              );
            }
          ),
        ],
      ),
      floatingActionButton: FloatingActionButton(
        onPressed: _incrementCounter,
        tooltip: 'Increment',
        child: Icon(Icons.add),
      ),
    );
  }
}

class OtherPage extends StatelessWidget {
  OtherPage(this.num);
  
  final int num;
  
  @override
  Widget build(BuildContext context) {
    print('build $num');
    return Scaffold(
      body: Column(
        mainAxisAlignment: MainAxisAlignment.center,
        children: <Widget>[
          FlatButton(
            child: Text('Push to ${num + 1}'),
            onPressed: () {
              Navigator.of(context).push(
                MaterialPageRoute(
                  builder: (_) => OtherPage(num + 1),
                ),
              );
            }
          ),
          FlatButton(
            child: Text('Pop to first'),
            onPressed: () {
              Navigator.of(context).popUntil((route) => route.isFirst);
            }
          ),
        ],
      ),
    );
  }
}