Unable to rewrite Drupal's node search to CSE search

We're making CSE our only search option by disallowing users from accessing Drupal's content search. By doing so, we also set up a rewrite rule as follows to accomodate any old links using the node search -

However, the rewrite only take you to the CSE search page without returning any results. The keyword does appear in the search box but you need to click the Search button again to get the results.

It's noted the rule indeeds rewrites a search on 'madoff' to
index.php\?q=search/google&cx=cxid&cof=FORID%3A11&query=madoff&op=Search

We're not sure this is a bug. But it would be nice if we can get the search results immediately as we would when using Drupal's default node search.

Thanks.