Using an Arduino (Mega ADK), how do I blink an LED on a separate IC (ATMega328) using SPI?
Although I am not very familiar with the Arduino, your sketch looks fine to me. But, there is something you are missing. ATMega328 is a microcontroller, just like your ATMega2560 on the Arduino. It is not an IC that is purposed to be controlled via SPI.

However, this does not mean that you cannot control this IC via SPI. Just like you did for your ATMega2560, you have to write code for ATMega328 to make it act like an "SPI Slave". Then, you will be able to make two microcontrollers speak SPI and they will communicate.

You have already configured ATMega2560 as an SPI Master, so your mission is half way complete. Now, you have to write code for ATMega328 and make it act like an SPI Slave. Then, on the slave side, you will check if master sends anything. And when master sends something to the slave, slave will check the bytes that you are sending, in this case 0x11 and 0x00 (and 0xFF for LED ON).

Learn how to write a sketch that configures ATMega328 as an SPI Slave, and learn how to receive data when it is configured as an SPI Slave. Then, you will check the data and act accordingly; for example, you will light up the LED when there is 0x11 and 0xFF code received.