Could quantum effects play an important role in the brain and the thought process?

Its a good idea, but it does not work that way. Also it depends on what quantom effects you are talking about. There are many different layers to this, and most of it is theoretical to begin with. And the small electrical pulses and not on a quantum level, this is hard to explain. There is a quantum level to everything, But that does not mean a lot. The act of thinking about two things at once and figureing which one is better is just problem solving, its a natural ability that our minds have. It has nothing to do with the way quantum particals react with our minds. Im sorry, I do understand what you are asking but as you said its difficult to make oneself clear on something of this level, ecpecially on a computer.