So I want to make a model of my character's head to put into my game as an accessory. He's a robot, who doesn't blink and doesn't move his lips when he speaks. (They're only for aesthetics really.) Here's a drawing of him, for reference's sake: http://i.imgur.com/bExaP.png

I could never pinpoint a tutorial that covered making hair/hats or accessories without adding skeletons and rigging them. Is it possible to just sculpt a model, make the textures, and plot them into the game?

No, but you can assign everything to one bone so that facial expressions don't do anything. If you don't assign the accessory to any bones at all, then in practise it crashes the game, while in theory it would just stay still and be left behind when the sim moved his head, sat down/stood up, walked away etc.

Also, thread moved to CAS parts.

I love the look of your character! If you want to make this as a 'head' that a sim will 'wear', and he doesn't need a moving mouth or eyes, just assign the whole mesh to the head joint (Head_New if you use Milkshape, don't know about other 3D apps) and package it as a Hat Hair.