We're currently using our Enterprise Search Center to search several file shares. We'd like to be able to add the capability for users to search their site collections for any files that are on that site collection. In order to do this, I assume we would need to crawl Local SharePoint sites. If this is the case, won't these then appear within our Enterprise Search Center? If that's the case, is there a way to hide Local SharePoint sites results from the Enterprise Search Center so that it only continues to search the file shares?
The Content Sources defined in the Search Service Application in Central Administration determine what the search engine should index/crawl. In your case, it sounds like you have a content source for your file shares and also the default "Local SharePoint sites" content source. The search engine can continue to index both these sets of content regardless of what you decide to surface to users. And yes, to crawl site collections you would need to ensure that your "Local SharePoint sites" content source includes the web application you'd like to crawl.
What your Search Center returns to your users is based on the Result Sources and the configuration of the web parts on the search pages in your Search Center. And underlying that configuration is the security -- users will not be shown content they don't have access to.
Update: Based on your comment you want to exclude all SharePoint site content. One way is to change your "Local SharePoint sites" content source so it doesn't crawl any more and the reset the index so only your file shares get crawled.
Another way as I mention above is to use a new Result Source. You'd create a new Result Source and when you build the query you'd use the ContentSource property to point to your file share Content Source. Then you need create or update your search pages and web parts to use the new Result Source.
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