Yep - sure will work.
I have an Xperia X10 running Android 2.1, and the Bluetooth picks up whatever audio output the phone is generating - games, movies, and yes, GPS (have done it with the Google Maps app).
And I thought I was going nuts! Same issue here - 2010 Limited rattles like crazy with the shade open. Something to add to the list of issues to take care of at the first oil change.