[Sync] Inject startup dependencies into StartupController.

components/browser_sync/browser/profile_sync_service.h

Index: components/browser_sync/browser/profile_sync_service.h
diff --git a/components/browser_sync/browser/profile_sync_service.h b/components/browser_sync/browser/profile_sync_service.h
index 430b919a827f5117a0c0521f1cc57c47f18dc90f..42949f0bb9ed48f0f58ffccad150443ab9aac0c8 100644
--- a/components/browser_sync/browser/profile_sync_service.h
+++ b/components/browser_sync/browser/profile_sync_service.h
@@ -754,6 +754,13 @@ class ProfileSyncService : public sync_driver::SyncService,
   // Whether sync has been authenticated with an account ID.
   bool IsSignedIn() const;
 
+  // The backend can only start if sync can start and has an auth token. This is
+  // different fron CanSyncStart because it represents whether the backend can
+  // be started at this moment, whereas CanSyncStart represents whether sync can
+  // conceptually start without further user action (acquiring a token is an
+  // automatic process).
+  bool CanBackendStart() const;
+
   // True if a syncing backend exists.
   bool HasSyncingBackend() const;