When you're falling asleep you can't dictate what happens to you, you just doze off regardless of where you are or what you are doing. Why would he make a temporary bed on the sofa? If he was tired he would have just gone to his bedroom.
Maybe he hadn't been watching the TV.
It wasn't a pillow, it was just a cushion on the sofa. His head was also partially resting on Leslie Winkle's violin case which further reinforces the fact that he accidentally fell asleep. You wouldn't purposefully go to sleep on a violin case - it would be extremely uncomfortable.
He probably just got cold while he was sat on the couch wondering what to do.
Surely you mean my theory is flawed? Which it isn't.