Added DataTypeController integration and UI surfacing for syncing Search Engines.

chrome/browser/resources/sync_setup_overlay.html

 <div id="sync-setup-overlay" class="page" hidden>
   <div id="sync-setup-login" hidden>
     <h1 i18n-content="syncSetupOverlayTitle"></h1>
     <div class="content-area">
       <div>
         <!-- top-blurb-error's reset state is handled differently from most
              elements. Instead of being [hidden] it is visibility:hidden so it
              still takes up space. But it is also [hidden] when we display the
              captcha, so when it is reset, it needs to be shown. -->
         <div id="top-blurb-error"
@@ skipping 288 matching lines @@
                       name="dataTypeCheckbox">
                   <label for="themes-checkbox" i18n-content="themes"
                       i18n-values="title:themes" name="dataTypeLabel"></label>
                 </div>
                 <div id="sessions-item" class="sync-item-show">
                   <input id="sessions-checkbox" type="checkbox"
                       name="dataTypeCheckbox">
                   <label for="sessions-checkbox" i18n-content="foreignSessions"
                       il8n-values="title:sessions" name="dataTypeLabel"></label>
                 </div>
+                <div id="search-engines-item" class="sync-item-show">
+                  <input id="search-engines-checkbox" type="checkbox"
+                      name="dataTypeCheckbox">
+                  <label for="search-engines-checkbox"
+                      i18n-content="searchEngines"
+                      il8n-values="title:searchEngines"
+                      name="dataTypeLabel"></label>
+                </div>
               </div>
             </div>
           </div>
           <div class="sync-configuration-errors">
             <div id="error-text" i18n-content="syncZeroDataTypesError"
                 class="sync-configuration-error reset-hidden" hidden></div>
             <div id="aborted-text" i18n-content="abortedError"
                 class="sync-configuration-error reset-hidden" hidden></div>
           </div>
           <div id="customize-sync-encryption">
@@ skipping 98 matching lines @@
       <span i18n-content="stopSyncingExplanation"></span>
     </div>
     <div class="action-area">
       <input id="stop-syncing-ok" type="button"
         i18n-values="value:stopSyncingConfirm">
       <input id="stop-syncing-cancel" type="button"
         i18n-values="value:cancel">
     </div>
   </div>
 </div>