Has anyone tried this? Can I stir small chunks of pre-made cookie dough into batter prior to baking for a 'Chocolate chip cookie dough' flavor? Or does the dough just bake and mix itself into the batter and kind of disappear?

I have read about putting a chunk of pre-made dough in cupcake centers. It's supposed to just bake into a nugget.
I would assume you'd need a nice thick dough so the chunks don't sink to the bottom like chocolate chips can.

I've done it with cupcakes but not a cake. I froze a ball of cookie dough and put it in the cupcake right before I baked it. It worked great. If the dough just bakes into the cake batter, maybe you could try freezing the dough first????

yeah, sounds good... maybe also shaking it in some cocoa poweder will also help to keep it in tact like choc chips...