This is a great idea for a plugin. Simple idea but so few people have done this. Every client I have heard from wants some kind of "subscribe to my blog" widget where people visiting their site can just type in an e-mail address and subscribe to a blog manually. They don't know what RSS feeds are and don't want to learn.
I tell them that no plugin has been developed yet to allow for this unless they use WordPress.com; at least none I can find through the Extensions section.
So...in conclusion...the widget may work, but be aware that if you try to use it as a widget you may have very long form spaces.