TheMadScientist - 7:06 pm on Dec 11, 2012 (gmt 0)
What tedster said, with the exception of when the person who built the custom 404 error page built it to guard against an .htaccess 'oops' (EG ErrorDoc http://example.com/404.php) and serves a 404 Not Found via server-side scripting which will override the 200 OK status the server would normally send, in which case a direct link to a custom error page would still be considered a broken link.
Status code makes the determination in most cases, so if the end result of the link results in the user-agent receiving a 404 Not Found status code, then the link is considered broken.
An exception to the status code being the determining factor is where a number of URLs end in exactly the same content (or no content), which is not a direct replacement for the original via redirect. This type of situation can cause the pages to be considered a 'soft 404' by search engines and would likely end up with them treating the links to the pages as broken.
There is really 'no such thing' as a totally blank page, because a properly functioning server will send a status code for every URL requested, so whether content is served to the browser or not doesn't really matter as much as the status code received (or derived as in the case of 'soft 404s') by the user-agent.