Unless the redesign is a major step backwards, where you'll lose a lot of users with the redesign.

The website for the card game Magic:the Gathering is an example of that, they absolutely wrecked their webpage and forums, and I know that they lost a lot of forum users and webpage readers because of that (but maybe it's ok for them if they weren't the core audience).

I don't know if they did gain among the younger audience, so maybe the redesign was a success... I'll never know, as I'm not an insider.