arc: Fix race when arc package sync service starts.

chrome/browser/ui/app_list/arc/arc_app_list_prefs.h

Index: chrome/browser/ui/app_list/arc/arc_app_list_prefs.h
diff --git a/chrome/browser/ui/app_list/arc/arc_app_list_prefs.h b/chrome/browser/ui/app_list/arc/arc_app_list_prefs.h
index a13aeb43554a5c47637f673aef2cc1cc3e022545..3676222f01327449914d171478f69378cb2b87e5 100644
--- a/chrome/browser/ui/app_list/arc/arc_app_list_prefs.h
+++ b/chrome/browser/ui/app_list/arc/arc_app_list_prefs.h
@@ -137,6 +137,8 @@ class ArcAppListPrefs
         const arc::mojom::ArcPackageInfo& package_info) {}
     // Notifies that package has been uninstalled.
     virtual void OnPackageRemoved(const std::string& package_name) {}
+    // Notifies sync date type controller the model is ready to start.
+    virtual void OnPackageListInitialRefreshed() {}
 
     virtual void OnTaskOrientationLockRequested(
         int32_t task_id,
@@ -232,6 +234,10 @@ class ArcAppListPrefs
     return app_instance_holder_;
   }
 
+  bool package_list_initial_refreshed() const {
+    return package_list_initial_refreshed_;
+  }
+
   std::unordered_set<std::string> GetAppsForPackage(
       const std::string& package_name) const;
 
@@ -359,6 +365,8 @@ class ArcAppListPrefs
   bool is_initialized_ = false;
   // True if apps were restored.
   bool apps_restored_ = false;
+  // True is Arc package list has been refreshed once.
+  bool package_list_initial_refreshed_ = false;
 
   arc::ArcPackageSyncableService* sync_service_;