Hmmm, the "Search Engine" itself is comprised of a number of associated scripts as well as several files containing the data to be searched. At least, that's my own understanding of it. The actual files involved are stored as many different files with names such as "package_0_xml.js" or "package_9_xml.js" and the numbers increment with the complexity of the help.
Storing all that information within the page itself would make for a very unwieldy page I would think. It would take a while for it to load into the browser.
But that's just being overly technical. My guess is that your company wants the actual field you type the search term(s) into to be somewhere on that page, right?
I think, technically speaking, Responsive HTML 5 does present a single page. So the technical answer would be that the Search field is already part of the displayed Topic.
Hopefully Willam will see this post and pop in to advise what may be possible here.
The HTML5 Charcoal Gray skin does have an option to show the search results over the topic contents. So that may get you part of the way. Look in the Search (Desktop) section for the item Search results in sidebar.
Adding the search to a topic is not supported. You can, alternatively, create a custom Layout page with only the search on it. That would replace your topic. This, however, is much easier said than done. The HTML5 Charcoal Gray is a single page output, so it's not easy to completely hook into all the functions.
An alternative would be to use Zoomsearch instead of the RoboHelp search. You can embed that in your topics. It would mean removing the search from the Charcoal Gray layout.