It is not necessary nor a good idea to replace the internal discourse search functionality.
However, there is nothing wrong with adding an additional search capability, Google or otherwise.
This is best done with a plugin and its own route / page.
My advice @KranthiKiranGude is to leave the discourse search feature as-is and create a plugin with a distinct page / route for GCS.
That is exactly what we did with our old LAMP forum, BTW.