I know this post is 11 years old. I have a 2013 Mazda 3 5 Door and when BT is connected on my Android Note 9 phone, I don't get any sound notification when a text message is received.
At first, I thought it was because I use Textra, and not the default texting app, but that's not the case.
I finally incorporated a workaround using an app called Tasker. I wrote a small Profile to beep when SMS received and BT Near Mazda. This is not perfect, but at least I know when I get a text message. I'd hoped that I could instruct Tasker to make my whistle sound, but it seems that even Tasker was sending stuff through BT when connected. So, I have Tasker Beep at a frequency of 8000 for 3591 milliseconds. I say beep, but it's more of a screech. I think the beep is sent to the phone's speaker and NOT through BT, which is why it works.
Here's a screenshot of the Tasker Profile Named "Beep when Text Received". Ignore the AOD and *ELEMNT Profiles:
Here's the Beep Task in Tasker:
And here's the Morse Task (which is not heard in the car, but I left it in there since the Beep works):
I hope this helps someone else, too. I lived with no audible text sound for 9 years before finally coming up with something...