This leads into the first big question for the new Apple TV. Do the settings include the ability to turn on/off captions. I've been looking through various photos and hands-on reviews but have yet to see if this is the case. If they do not have this setting, then you will not be able to get captions due to HDMI butchering CC data. Having said this, the AppleTV is based in iOS and CC on/off has been a setting on iPhones for a while, so it is likely to be there.
The next question is why is there so little CC content in the iTunes store? Apple made a big deal about captioning some movies a few years ago but has basically done very little since. You can see all the CC movies by going to Store -> Search -> Movies -> checkbox for CC. You won't be impressed. As far as I can tell, no TV shows are captioned.
This sort of problem has been going on since video sales were introduced in 2005. I have been told that at least one TV source claims to deliver shows to Apple with the CC data intact. Apple even has sample code in their Dev site for reading CC data:
http://developer.apple.com/library/mac/#samplecode/ClosedCaptionImporter/Introdu ction/Intro.html
Netflix has a similar problem in that they haven't been taking CC seriously either. They got called on the carpet for this at a shareholder meeting and have made slow, feeble steps towards providing captions since then. I suspect their AppleTV content will have similar deficiencies, assuming they even pass CC data to the AppleTV.
In short, this is a willpower thing, not a technical barrier. Until Apple, and Netflix, start importing CC by default we will continue to see very slow progress on this front.