Is it possible to control 600 Led with arduino Yun

This is what it should look like

The different rings represent each family member and where the ring lights up it means that this person will be home at that time.
This data comes from google calendar. And then this data will be converted to the the What Led should light up with the arduino.
The arduino yun has an ethernet shield. So i can get the google data.
The data can than be saved on the arduino's flash memory i Guess.
But my main question is if I'm going to have trouble sending so much data to so much LEDS, because i think i need my ram to run the program and all the data that needs to be send already takes 1.8 kb or more. so i have only 0.7 kb left.
Is this to few?
And I don't need verry fast performances to refresh the LEDS do i have a problem then with sending so much data?
I don't care if it takes a second or 1 millisecond to refresh all the leds.