Basically correct but again your words show the wrong thinking:-
im assuming each LED will suck whatever voltage they need from the 12volts.
They don't suck voltage out of anything. They develop voltage across them. So with 12 volts supply you have 12V to spread over everything in series. If the LEDs drop 3.6V each then 3 of them will drop 3.6 * 3 = 10.8V, your resistor will take a voltage = I * R and the rest will drop across the regulator. You just have to make sure that this is enough so that the regulator still works (it's in the data sheet)