No the PC doesn't need to be hooked up to the HAI.
You need a PIM hooked to the PC.
It will receive all of the traffic on the UPB network regardless of source (HAI, local switches, other controllers).
Even using HLC and all HAI components, it's still a good idea to have a second standalone PIM and a copy of UPStart to program non-HLC behaviors and for troubleshooting/archiving UPB network setups.
As far as I know there is no way to directly log what the HAI is transmitting. Even if you were to add programming lines to log UPB transmissions, a lot of those transmissions are automatically sent in response to other traffic so it would be very difficult to capture them all.