[Sync] Fix sync backup for supervised users

sync_initialized() does not account for backup/rollback modes. For now we
just manually check the backend mode. In the future the PSS will expose
a better method for denoting when its safe to reconfigure.

BUG=417400

Review URL: https://codereview.chromium.org/605483002

Cr-Commit-Position: refs/heads/master@{#296968}

chrome/browser/supervised_user/supervised_user_service.cc

@@ -413,7 +413,8 @@ syncer::ModelTypeSet SupervisedUserService::GetPreferredDataTypes() const {
 void SupervisedUserService::OnStateChanged() {
   ProfileSyncService* service =
       ProfileSyncServiceFactory::GetForProfile(profile_);
-  if (waiting_for_sync_initialization_ && service->sync_initialized()) {
+  if (waiting_for_sync_initialization_ && service->sync_initialized() &&
+      service->backend_mode() == ProfileSyncService::SYNC) {
     waiting_for_sync_initialization_ = false;
     service->RemoveObserver(this);
     FinishSetupSync();
@@ -444,7 +445,8 @@ void SupervisedUserService::FinishSetupSyncWhenReady() {
   // Continue in FinishSetupSync() once the Sync backend has been initialized.
   ProfileSyncService* service =
       ProfileSyncServiceFactory::GetForProfile(profile_);
-  if (service->sync_initialized()) {
+  if (service->sync_initialized() &&
+      service->backend_mode() == ProfileSyncService::SYNC) {
     FinishSetupSync();
   } else {
     service->AddObserver(this);
@@ -455,7 +457,8 @@ void SupervisedUserService::FinishSetupSyncWhenReady() {
 void SupervisedUserService::FinishSetupSync() {
   ProfileSyncService* service =
       ProfileSyncServiceFactory::GetForProfile(profile_);
-  DCHECK(service->sync_initialized());
+  DCHECK(service->sync_initialized() &&
+         service->backend_mode() == ProfileSyncService::SYNC);
 
   // Sync nothing (except types which are set via GetPreferredDataTypes).
   bool sync_everything = false;