The micro USB Y-cable comes with the BSP. It's official purpose is to avoid ground loops when using analog gear with a computer, but just happens to be necessary to get iPad to talk to it (thanks Apple...)
I just checked with Ableton live lite 8 in windows 7 - if I plug a midi keyboard into the BSP, even in control mode Ableton only receives single notes with no pitch or modulation control. If I record MIDI from the BSP in ableton and throttle the pitch knob up and down, nothing is recorded. If I plug the same keyboard into a MIDI-USB cable and connect it to the computer, ableton registers poly notes and if I record just throttling the pitch knob, you can see the pitch bend envelope in the clip view.
Sorry to say it doesn't appear to record controls, at least I couldn't figure it out anyway.
As far as recording on the BSP, it doesn't seem to record anything in control mode. When in sequencer mode, turning the knobs only changes the note of the a particular step, but that can be done without being in record mode. Of course recording is most useful to play a sequence on the pads or from an external keyboard, but obviously it will be monophonic and quantized to the steps (with velocity & gate time).
Don't let me put you off though! As a beginner I've learned more in 5 minutes with the BSP than the hour I spent the first time I tried to get a sound out of Ableton. I guess the idea of a sequencer like this is so that you have the time and focus to be able to tweak your filters and envelopes while it churns out the loops. Plus if you're a hopeless non-musician like me you can record a pattern and then fine tune it back into something intelligible!