Ok, this lets me know how your head unit is currently coded.
Yes, if you install the Bose system, it will just work without any coding changes. The line-level outputs from the head unit will be 'too hot' for the Bose amp's inputs, meaning you'll not have great volume control resolution and you'll easily clip the inputs if you're not careful. Also, the EQ will be a bit wrong. However, you'll be able to test your physical installation.
I hope that makes sense. When I'm not working on A2s, I'm an audio systems engineer, so I don't know how much of the above is subject-specific jargon!
Cheers,
Tom