No, connecting it that way would mean you would be recording unprocessed, not processed.
If it gets confusing, draw a schematic on paper first, laying out exactly how you want the signal to go. It will make much more sense.
Breakaway cannot send to a pipeline and the soundcard at the same time, so you must send Breakaway Output to a pipeline. You can then download the free version of Virtual Audio Cable from http://software.muzychenko.net/eng/vac.html and use the program Audio Repeater from there, to also send the pipeline audio to the sound card.
///Leif