Do custom error pages return 404 headers?

I removed some pages from my website but those pages are still indexed by search engines. So I have set-up a general custom error page using web.config and the defaultRedirect property. Over time I want those broken indexed links to be removed from search engines. I know that search engines remove the indexed pages if there is a 404 error returned.

My question is that, when search engines crawl my website and receive the custom error page, will the server return a 404 header to the search engine causing it to not indx my page?
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