We can add search center for SharePoint site in google chrome as regular google search for SharePoint site. Here we are just creating a custom search engine by passing SharePoint search site Url as shown below.
Navigate to google chrome and right click on the address bar, Select “Edit search engines” option
In “Search Engine” dialog box, other search engine division we have to fill Search Engine Name, Keyword, Url. Google chrome will use default site domain name . In keyword section enter SharePoint Search for easy understanding. In URL, enter the search URL and assign “%S” at the end. Click on Done button to save the search engine settings.
To search the details, write, “SharePointSearch” in browser address bar and press tab to enter the search query. Here I am entering Suresh and result will display as the images.