For me the 2-minute rule applies only when I have the 2 minutes. If I'm in the middle of something else and think of an unrelated idea, I will jot it down quickly. I'm loath to interrupt my current momentum, other than to quickly get things out of my head as they come to me. The 2-minute rule only comes into consideration when I begin processing.
I, too, use daily checklists, although I believe I have quite a way to go in that area, compared to other GTDers on this forum.