CPU, iOS, and Chat all seem to fall under the branch of "At-Home Adviser". You're just placed into departments. What I can gather from prior posts is that the position isn't easy, requiring five chats at once and management of this position is stricter since Chat Logs are easier to skim through than Voice Call Logs.
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Training, in general, covers the tools you'll be using as well as the finer points and regulations of support in your department. I'm sure you'll touch on some iOS points. However this is all speculation, and probably the best response without searching for it, since all who join on with Apple are under NDA.
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For those interested, and since I'm bored waiting for BGC, I managed to dig up some photos via Twitter of someone who posted AHA stuff. Namely themselves and the iMac, which happens to be displaying adviser tools.
The photo of the headset is pretty easy to find, as is the iMac image, so I don't think I'll get too much flac for posting it, however I'll remove it as soon as someone says anything about it.
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Not much there to see.. a group chat, someone's work schedule... nothing that would set off NDA alarms. What you'll be seeing most of the time while working is iLog, the call logging software(not seen in the picture).
I can't speak for iTunes chat but we just had someone transfer over to iOS chat support and they said that the max number of concurrent chats they do is 2. iTunes by far is the busiest support group so they may or may not have more than 2 chats going on at once.
All I'm gonna say is think carefully before jumping into iTunes support.