For example, a message could be something like ‘Dinner is ready’.
Yes, this will work, and it is actually how the Amazon Echo and Fire Stick/Fire Cube are designed to function!
If you make an announcement using any Alexa device in your household, the message will also play on your Fire device, along with a pop up of the message.
I just tested this by making an announcement with my Echo, which then played the audio through my Fire Stick and then flashed the message up on the screen (very briefly!). I didn’t know this was possible before but this is a good feature to know about!