Technically speaking, it is not required, but it's a good idea to have an email on record for practical reasons. If there is no e-mail on record, there is no way for you, as an admin, to contact that user. Many websites require you to enter an email address when you sign-in with twitter. Some examples are [Drywall](https://drywall.onmodulus.net), [LiveJournal](http://www.livejournal.com/).