I was wondering that myself.
It should work if
1. Your AVIC N3 has the ability to work with a steering wheel control adapter AND
2. The connections in the back of your AVIC N3 matches up with the B connector-and I'm guess it will because the B connector takes the role of the A connector that is coming from the car. So as long as the AVIC N3 installation doesn't require you cutting out your car's original A connector and splicing an aftermarket connector that matches the input of the AVIC N3 then you should be fine.
That said, I always assumed those fancy $799 to $1499 AVIC units already came with bluetooth?