The point of LANnouncer is that it doesn’t have to run on the phone you use every day. In fact it probably wouldn’t because most people prefer their announcer device to stay at home. (you can get push notifications on your regular phone as well if you want the alert that way)
So that instead of buying the $49 Aeon doorbell you could buy a $40 android tablet and it becomes your speaker device.
So you can think of that as a device option rather than as an app option. You might still prefer the doorbell device, but it’s always good to have choices. 
Not quite sure I understand your question of whether the Aeon doorbell “will work with the Samsung system.”
Were you asking if that device can be controlled from SmartThings? If so, definitely. It’s a certified Z wave device. The link in the wiki article takes you to discussion of the device type handler that works with it. If you haven’t had a chance to follow that link yet, here it is:
Remember that that device can be used in two different ways. It comes with its own physical button, so it can be used that way.
But you can also play any of its 99 tracks by sending a command from the smartthings hub. So that’s how it fits into a SmartThings system. You can set up a rule so that if the front door sensor is opened, the sensor tells the hub and the hub tells the doorbell device to play track 17 or whatever. You can play a different track for a sensor on the back door. Still another track when someone pushes a button on a handheld device. Or pretty much anything you can think of that is triggered by an event that the smartthings hub can recognize.
I hope that helps clarify it. If you have any further questions about the Aeon doorbell itself, you can ask them in the thread at the link above in this post. Those are the people who are using it every day.