Add base::RunLoop and update ui_test_utils to use it to reduce flakiness

ui/aura/desktop/desktop_dispatcher_client.cc

 // Copyright (c) 2012 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #include "ui/aura/desktop/desktop_dispatcher_client.h"
 
+#include "base/run_loop.h"
+
 namespace aura {
 
 DesktopDispatcherClient::DesktopDispatcherClient() {}
 
 DesktopDispatcherClient::~DesktopDispatcherClient() {}
 
 void DesktopDispatcherClient::RunWithDispatcher(
     MessageLoop::Dispatcher* nested_dispatcher,
     aura::Window* associated_window,
     bool nestable_tasks_allowed) {
   // TODO(erg): This class has been copypastad from
   // ash/accelerators/nested_dispatcher_controller.cc. I have left my changes
   // commented out because I don't entirely understand the implications of the
   // change.
   MessageLoopForUI* loop = MessageLoopForUI::current();
   bool did_allow_task_nesting = loop->NestableTasksAllowed();
   loop->SetNestableTasksAllowed(nestable_tasks_allowed);
 
   // DefaultAcceleratorDispatcher dispatcher(nested_dispatcher,
   //                                         associated_window);
-  loop->RunWithDispatcher(nested_dispatcher);
+  base::RunLoop run_loop(nested_dispatcher);
+  run_loop.Run();
   loop->SetNestableTasksAllowed(did_allow_task_nesting);
 }
 
 }  // namespace aura