To answer your question plainly. If your dns server goes down and everything else is up....people still will not be able to get to the sites or receive email..unless they are using IP addresses rather than names (not likely)
What we do is we have DNS running on 3 servers. Two in PA and one in TX. All of our domain names...with the exception of a few resellers....are hosted on all 3 servers either in a primary or secondary role.