As a matter of fact, yes you can. I was looking for the same thing and the link from your question lead me to this from Google Blogpost
Anyhow, below are my layout files, as for java code I did not change anything and Fragment calling remains the same.
activity_main.xml (Main file)
<?xml version="1.0" encoding="utf-8"?>
<android.support.v4.widget.DrawerLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:id="@+id/drawer_layout"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:fitsSystemWindows="true"
tools:openDrawer="start">
<include
layout="@layout/app_bar_main"
android:layout_width="match_parent"
android:layout_height="match_parent" />
<android.support.design.widget.NavigationView
android:id="@+id/nav_view"
android:layout_width="wrap_content"
android:layout_height="match_parent"
android:layout_gravity="start"
android:fitsSystemWindows="true"
app:headerLayout="@layout/nav_header_main"
app:menu="@menu/activity_main_drawer" />
</android.support.v4.widget.DrawerLayout>
app_bar_main.xml (NavigationBar layout)
<?xml version="1.0" encoding="utf-8"?>
<android.support.design.widget.CoordinatorLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:layout_width="match_parent"
android:layout_height="match_parent"
tools:context=".MainActivity">
<android.support.design.widget.AppBarLayout
android:layout_width="match_parent"
android:layout_height="192dp"
android:theme="@style/AppTheme.AppBarOverlay">
<android.support.design.widget.CollapsingToolbarLayout
android:id="@+id/toolbar_layout"
android:layout_width="match_parent"
android:layout_height="match_parent"
app:layout_scrollFlags="scroll|exitUntilCollapsed">
<android.support.v7.widget.Toolbar
android:id="@+id/toolbar"
android:layout_width="match_parent"
android:layout_height="?attr/actionBarSize"
android:background="?attr/colorPrimary"
app:layout_collapseMode="pin"
app:layout_scrollFlags="scroll|enterAlways"
app:popupTheme="@style/AppTheme.PopupOverlay" />
</android.support.design.widget.CollapsingToolbarLayout>
</android.support.design.widget.AppBarLayout>
<include layout="@layout/content_main" />
<android.support.design.widget.FloatingActionButton
android:id="@+id/fab"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_gravity="bottom|end"
android:layout_margin="@dimen/fab_margin"
android:src="@android:drawable/ic_dialog_email" />
</android.support.design.widget.CoordinatorLayout>
content_main.xml
<?xml version="1.0" encoding="utf-8"?>
<android.support.v4.widget.NestedScrollView xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:paddingBottom="@dimen/activity_vertical_margin"
android:paddingLeft="@dimen/activity_horizontal_margin"
android:paddingRight="@dimen/activity_horizontal_margin"
android:paddingTop="@dimen/activity_vertical_margin"
app:layout_behavior="@string/appbar_scrolling_view_behavior"
tools:context=".MainActivity"
tools:showIn="@layout/app_bar_main">
<FrameLayout
android:id="@+id/content_main_frame"
android:layout_width="match_parent"
android:layout_height="match_parent" />
</android.support.v4.widget.NestedScrollView>
And now you have "DrawerLayout + Fragments + CollapsingToolbarLayout"