Fetch a new GAIA picture every time chrome://settings/manageProfile comes up.

chrome/browser/profiles/avatar_menu_actions_desktop.cc

 // Copyright 2013 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #include "chrome/browser/profiles/avatar_menu_actions_desktop.h"
 
 #include "base/compiler_specific.h"
 #include "base/strings/string_number_conversions.h"
 #include "chrome/browser/browser_process.h"
 #include "chrome/browser/profiles/profile.h"
@@ skipping 31 matching lines @@
   if (!settings_browser) {
     const Browser::CreateParams params(ProfileManager::GetLastUsedProfile(),
                                        chrome::GetActiveDesktop());
     settings_browser = new Browser(params);
   }
   chrome::ShowSettingsSubPage(settings_browser, chrome::kCreateProfileSubPage);
   ProfileMetrics::LogProfileAddNewUser(type);
 }
 
 void AvatarMenuActionsDesktop::EditProfile(Profile* profile, size_t index) {
+  profiles::UpdateGAIAProfilePhotoIfNeeded(profile);
+
   Browser* settings_browser = browser_;
   if (!settings_browser) {
     settings_browser = new Browser(
         Browser::CreateParams(profile, chrome::GetActiveDesktop()));
   }
   std::string page = chrome::kManageProfileSubPage;
   page += "#";
   page += base::IntToString(static_cast<int>(index));
   chrome::ShowSettingsSubPage(settings_browser, page);
 }
@@ skipping 13 matching lines @@
 #if defined(OS_WIN)
   return chrome::GetActiveDesktop() != chrome::HOST_DESKTOP_TYPE_ASH;
 #else
   return true;
 #endif
 }
 
 void AvatarMenuActionsDesktop::ActiveBrowserChanged(Browser* browser) {
   browser_ = browser;
 }