What to you mean by searchable?
I’m guessing but if you mean that you want to search the contents of the post object like they are part of the post you’re adding them to in the repeater field, then this is not possible. The only thing that ACF stores is the post ID of the selected post. All other data is related to that post. Searching in WP is limited to the content and meta fields of the post and there are no applications that I know of that will let you search.
It’s like this
