While in the waking state, does it help (your spiritual growth) to be more aware of your body, the environment?

(Yes), to try to expand your awareness more and more. That’s a good practice, because grace comes with self effort. Even in the normal sense we have the capacity to become more aware, maybe not more spiritually aware, but more aware.
When the observer becomes more spiritual then more love comes into the field and more peace comes into the field and more intuitive insights come into the field. If you start (observing) from the material point of view it can help you jump to the more spiritual point of view if you have contact with a guide.

Literally being in the now means trying to be in the moment but to wake up from the dream means to really understand all of what is happening around you. To understand that requires a consciousness jump to a different way of seeing.
Understanding the meaning and purpose of every event that is happening in the “now” can help you wake up, that’s where transformation takes place.