I find that hard to believe...or at least, the first part you said. Imagine not knowing any English, being shoved into America, or more specifically, a small town in America where no one speaks any language that you understand. The only way they have to convey things to you is through body language and pictures (which was the first human language anyways). You would have the nice advantage of having someone point to a vase and say "vase" or point to a fridge and say "fridge" or draw a picture of someone running and say "run". You don't have this with anime. Most of what is said does not apply to the pictures being shown on screen nor are they pointing to nouns or making pictures of verbs or adjectives and telling you what they are. Without independent study based on what you have seen in the anime, I would venture to say you only get a handful of vocab, very little if any grammar, and maybe a decent number of common phrases that you may or may not know the different subtle meanings to. Maybe I'm just thinking about this in the wrong way...anyone care to explain it to me from a different perspective?
I forgot to mention that watching anime nonstop without subs when you don't know what is being said is also a great way to ruin some good series, as well as it is very boring to just watch someone speaking nonsense all day that you don't understand 
Of course, I wasn't really suggesting that watching anime 24/7 is a viable way to learn. But being completely immersed in an environment, is exactly how you learned your first language.
I know it seems strange, but just listening passively is how you learned 99% of your vocabulary. For sure, body language did help for words like 'mummy' and 'daddy', and some other nouns you might have been 'pointed' at. But did you get any assistance in body language, being 'taught' how to say 'my name is *insert name*'? Nup, there was no help there, not even people talking it to you in baby talk and expecting you to repeat back. You learned how to say it just by hearing people around you say it, to each other, as native speakers of the language.
And of course, babies learned by doing this. Dumb babies! Honestly, have you seen how dumb they are? Their brains are TINY! Adults have the power to think about things, and to fit together any rules of grammar they might pick up. So, I'd even say that it would work even better for adults, if you chose to literally watch it, live it and breathe it every second of your life for a year or two. You already have a language down in your head, so you know how at least one language works, and you have a lot more intelligence than babies.
Although this is how the AJATT method works. Of course, while Khatz says to immerse yourself 24/7, adults (and students) have busy lives, and can't be completely focussed on the input they are receiving. But just having it in the background playing helps towards assimilating the language.
Oh, and on a final note, I always watch an anime with subs the first time round. I'm currently going through Clannad and Gundam SEED subbed, first time round. But after I've finished a series, I'll always rewatch it. Usually never straight afterwards, or even in the right order. This will of course change, when I can listen well enough to get a decent hold on what's going on without subs. Boring, rewatching anime? I don't think so, especially when you're concentrating on the language the second time around. And notice, I've only got a few series, so might as well make the most of my DVD money
