Haven't tried running an IDN name on EPi but I'd say that you're better off just doing redirects from the IDN-name website.
It's always wise to keep one name as primary and do redirects off all other names - and with that I also include the "non www."-name.
There are actually some central parts in EPiServer that still use the URL schema when dealing with links. This means that some parts will not work with IDN:s and IRI:s. I have not heard much complaints about this, though it appears from time to time, so guessing that Johans approach is the way to deal with this.
I have tried to configure a EPiServer web site with Swedish characters in the URL. E.g. http://båtar.example.com should work as well as http://batar.example.com
What I've tried is to add the Swedish address in the host names section for the website settings. It works partly in edit mode but not in normal view, i.e http://båtar.example.com/epi/cms works for the root page but not for any child pages or view mode.
Should it be possible, or do I need to make a redirect from another site to my EPiServer site?