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

chrome/browser/resources/options/browser_options_profile_list.js

 // Copyright (c) 2012 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.
 
 cr.define('options.browser_options', function() {
   /** @const */ var DeletableItem = options.DeletableItem;
   /** @const */ var DeletableItemList = options.DeletableItemList;
   /** @const */ var ListSingleSelectionModel = cr.ui.ListSingleSelectionModel;
 
   /**
@@ skipping 99 matching lines @@
     deleteItemAtIndex: function(index) {
       if (loadTimeData.getBoolean('profileIsManaged'))
         return;
       ManageProfileOverlay.showDeleteDialog(this.dataModel.item(index));
     },
 
     /** @override */
     activateItemAtIndex: function(index) {
       // Don't allow the user to edit a profile that is not current.
       var profileInfo = this.dataModel.item(index);
-      if (profileInfo.isCurrentProfile)
+      if (profileInfo.isCurrentProfile) {
+        chrome.send('refreshGAIAPicture');
         ManageProfileOverlay.showManageDialog(profileInfo);
+      }
     },
 
     /**
      * Sets whether items in this list are deletable.
      */
     set canDeleteItems(value) {
       this.canDeleteItems_ = value;
     },
 
     /**
      * If false, items in this list will not be deletable.
      * @private
      */
     canDeleteItems_: true,
   };
 
   return {
     ProfileList: ProfileList
   };
 });