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

components/precache/content/precache_manager.cc

Index: components/precache/content/precache_manager.cc
diff --git a/components/precache/content/precache_manager.cc b/components/precache/content/precache_manager.cc
index 327fa2b6b83ceafdd748f932467358cb30803ee7..6315bf22069307ec080ffdb92239bab30e36de16 100644
--- a/components/precache/content/precache_manager.cc
+++ b/components/precache/content/precache_manager.cc
@@ -103,10 +103,11 @@ PrecacheManager::AllowedType PrecacheManager::PrecachingAllowed() const {
     return AllowedType::PENDING;
 
   // SyncService delegates to SyncPrefs, which must be called on the UI thread.
-  if (history_service_ &&
+  if (history_service_ && !sync_service_->IsLocalSyncEnabled() &&
       sync_service_->GetActiveDataTypes().Has(syncer::SESSIONS) &&
-      !sync_service_->GetEncryptedDataTypes().Has(syncer::SESSIONS))
+      !sync_service_->GetEncryptedDataTypes().Has(syncer::SESSIONS)) {
     return AllowedType::ALLOWED;
+  }
 
   return AllowedType::DISALLOWED;
 }