If I understand your question correctly, then yes, the unit will stream audio from your phone; however, it relies on the older OnStar architecture of the vehicle and only streams in mono. I believe it is specifically the left channel (someone please correct me if I am wrong). This is, as I understand it, a limit of the OnStar system and not something that can be overcome with a firmware update. To receive stereo streaming, you must run a cable from the unit to the aux port of your vehicle. Assuming your vehicle has one, which mine does not.
If you are dealing with a vehicle such as mine--which does not have any sort of aux port--and do not wish to drill holes and run wire, I can provide a suggestion which as worked well for me. Most phones have the ability to output in mono only. You can usually find this setting under the accessibility options. I believe it is meant for those who are deaf in one ear and so need both channels to be pumped through a single side of a set of headphones. However, it also works wonderfully for the purposes of using the Costar as-is to stream music. Perhaps there are some people who will scoff at the sound quality that results, but I would argue that your average person will not be able to tell any appreciable difference. If it is a serious issue for you, then feel free to run wires to your heart's content.