I would say no. The noting is an early practice when habits of presence aren't developed enough yet. You can go very far, but the noting can get in the way of just pure acknowledgement, when you get more advanced.

I think noting is required still when you have a few gaps where the mind is blacking out and not seeing the cause and effect, and the suffering. So it's really good to note things that you haven't noticed about your mental movements. Noting things that your awareness picks up on its own from practice won't be as important in later stages as noting what you've been missing the whole time. Note what feels like a self, dissatisfaction, and impermanent. This can be done by noting gones and feeling their sense of rest.

The dispassion is what gets you there. This is why concentration is a big part of the practice. Sticking with things and gradually reducing the effort so it's not too much or too little.

You might want to read (or re-read if you already have) the "A Revised Four-Path Model'" section of MCTB2. He mentions the difficulty of third path onwards and lays out some strategies for untangling the knot of perception for the higher paths; strategies that go beyond noting.