TPAACAudioConverter's not well suited for live recording, just because of the way it's structured, pulling audio from a delegate instead of offering the ability to send audio to it directly.
I recommend using the ExtAudioFile services directly, as it already does the work for you.
If you really have to use TPAACAudioConverter, you'll need to use a ring buffer (like TPCircularBuffer) to store audio until TPAACAudioConverter retrieves it via the delegate method. It's messy though; use ExtAudioFile.
For the record, The Amazing Audio Engine contains a very simple mechanism for recording straight to AAC, or any other supported format. It'll be out soon.