Reminders app doesn't show badges
Unfortunately, it doesn't appear to, no: the Reminders app has neither its own  pane in the Settings app, nor any settings accessible in the app itself, and its entry under Notifications doesn't have an option to turn on Badges.

So, at least as of iOS 5.0.1, Reminders doesn't seem to support that feature.

I'm not seriously suggesting you switch apps, but if Badges in a todo app is a killer feature, I've also been a fan of Things.