It needs to go into the Screen Layout (Topic.slp) of the layout. But it's a bit more complicated. The RH search is integrated with the layout and all kinds of events are handeled when a search is started: search results are made visible, other panes will be closed, etc. And then you have the option to show search results in the sidebar or in the topic area.
The easiest try is to replace the search field in the Topic.slp with the Google snippet and replacing the Search results widget in the Topic.slp. Perhaps t works. But I haven't tried it with RoboHelp before.
In the layout, search for 'wSearchField': that will get you the search input field.
Search for: '<?rh-msp-search-results-start' that will get you the start of the search results code