[Sync] Refactor non-frontend DTC to handle new API properly.

chrome/browser/sync/glue/change_processor.h

Index: chrome/browser/sync/glue/change_processor.h
diff --git a/chrome/browser/sync/glue/change_processor.h b/chrome/browser/sync/glue/change_processor.h
index 2c581c93422d3f3c997706a35edc31db4a64bfb6..1b6b976963eaea47210ea56405213391433127df 100644
--- a/chrome/browser/sync/glue/change_processor.h
+++ b/chrome/browser/sync/glue/change_processor.h
@@ -75,9 +75,9 @@ class ChangeProcessor {
   virtual void StartImpl(Profile* profile) = 0;
   virtual void StopImpl() = 0;
 
-  bool running() { return running_; }
-  UnrecoverableErrorHandler* error_handler();
-  virtual sync_api::UserShare* share_handle();
+  bool running() const { return running_; }
+  UnrecoverableErrorHandler* error_handler() const;
+  virtual sync_api::UserShare* share_handle() const;
 
  private:
   bool running_;  // True if we have been told it is safe to process changes.