I can't see why the satnav would take its power from the Bose but I don't have a birdview so can't say for sure
The problem is the output from the satnav for the sound, I don't think it is standard, it may well be part of the loom but unless you can identify it and connect it to the mute input on the HU you will struggle, as with most things I am sure someone else has tried and hopefully managed it
I had never messed with car audio before I got my Zed, now I have more ICE than a Polar Bear
Have you taken anything apart yet, obviously you could dissconect the Bose then try the ignition and see if the satnav fires up