Hello Tarun,
Omni search is indeed quite useful and the improvements are nice in AEM 6.2 and also in AEM 6.3.
The links you mention do indeed show how to use this on the Author environment.
Omnisearch is largely based on Coral UI and in that sense it would not be possible to use it in the publish environment. The limits of using Coral UI are described on this page: Concepts of the AEM Touch-Optimized UI
There it says, "Use of Coral UI is only permitted: For use when extending the existing UI of the authoring environment."
There are many ways to build a search for the Publish environement and there are some examples in the Geometrixx implementation. You can also find some basic information on implementing a search tool here: Search
Cheers,
Stephan