Disabling Sync shouldn't prevent GaiaInfoUpdate.

Right now --disable-sync disables a lot of signin; any signin errors aren't surfaced, because nothing attempts to ping GAIA. This will help address that.

BUG=NONE
TEST=Run Chrome with the --disable-sync flag. Sign into a Profile and
the name (from G+) should appear in the Avatar Menu.

Review URL: https://codereview.chromium.org/870803003

Cr-Commit-Position: refs/heads/master@{#313557}

chrome/browser/profiles/gaia_info_update_service.cc

@@ -14,7 +14,6 @@
 #include "chrome/browser/profiles/profile_metrics.h"
 #include "chrome/browser/profiles/profiles_state.h"
 #include "chrome/browser/signin/signin_manager_factory.h"
-#include "chrome/browser/sync/profile_sync_service.h"
 #include "chrome/common/pref_names.h"
 #include "components/signin/core/common/profile_management_switches.h"
 #include "content/public/browser/notification_details.h"
@@ -70,10 +69,6 @@ bool GAIAInfoUpdateService::ShouldUseGAIAProfileInfo(Profile* profile) {
   return false;
 #endif
 
-  // Sync must be allowed.
-  if (!profile->GetOriginalProfile()->IsSyncAccessible())
-    return false;
-
   // To enable this feature for testing pass "--google-profile-info".
   if (switches::IsGoogleProfileInfo())
     return true;