[Sync] Allow sync start without sign-in if the local sync backend is on.

chrome/browser/ui/sync/sync_promo_ui.cc

 // Copyright 2013 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 "chrome/browser/ui/sync/sync_promo_ui.h"
 
 #include "chrome/browser/profiles/profile.h"
 #include "chrome/browser/signin/signin_promo_util.h"
+#include "components/sync/base/sync_prefs.h"
 
 bool SyncPromoUI::ShouldShowSyncPromo(Profile* profile) {
   // Don't show sync promo if the sign in promo should not be shown.
   if (!signin::ShouldShowPromo(profile)) {
     return false;
   }
 
-  // Don't show if sync is not allowed to start.
-  if (!profile->IsSyncAllowed())
+  syncer::SyncPrefs prefs(profile->GetPrefs());
+  // Don't show if sync is not allowed to start or is running in local mode.
+  if (!profile->IsSyncAllowed() || prefs.IsLocalSyncEnabled())
     return false;
 
   return true;
 }