As I understand it, the emergency alert messages that you get in the UK and AUS systems (which I assume is also the system we will adopt) are not text messages. Thus it's not a question of them overriding your setting for text messages; they're not affected by those settings in the first place. They are affected by your general settings (e.g. if your phone is on silent) and they will override those.
If you receive one of these messages your phone doesn't read it out aloud - at least, not by default. There's an audible signal to alert you, but you have to read the message on the screen.
If you have your phone, or your car entertainment system linked to your phone, configured to read out text messages by default, I don't know whether this configuration will also apply to these alerts. This may vary from system to system. I also don't know if you can separately configure to have emergency alerts read out loud, even if texts are not.
The bottom line is that they are intrusive — that's a feature, not a bug — and they do risk posing a distraction to drivers. Nevertheless, if there's an imminent danger that requires people to take prompt action, I think the distraction is justified. We don''t ban car systems that do, in fact, read out all your text messages, or offer audibly to do so, or that allow you to make and receive hands-free calls, and these are also distracting, and don't serve the same safety goals.
The point is that these urgent alert systems should only be used to convey messages that do require immediate action to avert or avoid a danger. "Don't light barbecues today" is not such a message, but "there's a car, quite close to you, that is driving at speed the wrong way down the motorway that you may currently be on" certainly is.
Whether you get the message or not depends on what mobile phone tower your phone is connecting to, so messages can be delivered in a highly localised way. The system is not precise enough to deliver the message only to people who are in the affected carriageway, but it certainly precise enough only to deliver the message to people who are within a kilometre or so of the location of the offending vehicle, or of its apparent course. But all phones in the selected area will get the message, including the phones of people who are not driving on the motorway, or who are not driving at all.