48V DC Power Supply Using LM7812 in Series
No, what you proposed won't work, and here's why. 


15V at 3A is 45W, not 600W. Your input power is insufficient, so adding pass transistors will do absolutely nothing for you.
You cannot stack 4 12V regulators on top of each other unless they are isolated. With one transformer they would not be. Youu would be shorting the 12V output to ground.
The 78xx series' output current is 1A max. 600W would require 12.5A, 1250% over spec.
Let's pretend you could get it to work and it was 70% efficient (good for a linear supply). That means you would have over 200W of heat to get rid of. That would take some enormous heatsinks.


You really need to look at some sort of offline switching regulator for that kind of power.