Of course. Self awareness is being aware of your existance, and we exist in the real world. We cannot neglect the environment when practicing self awareness. We should look at the environment as the place we exist and effect, and be aware of what existance is. We evolved to having self awareness, and being self aware means being aware of our current state of existance, meaning we know when the environment around us is from our creation because we have awareness of OUR presence.
Essentially, practicing self awareness means nurturing a sense of awareness of our existance and our effect and that sense makes us lucid during dreams because we know our existance now is in the dream. It is different than ADA environmental awareness that is being aware of entities. Self awareness is the awareness of ME, so we know when the environment around us revolves around ME(dream).
Hope I made sense.

So, self awareness is like an alert that detects when WE are not in the usual world where we are being effected and are effecting.