I read about this in some magazine years ago and I started doing it. They called it doing a "water wash". I don't even know how long it takes me.
I use warm water and totally soak my hair from root to tip. I then lean to the right and gently twist into a ponytail to lightly squeeze the water out. I lean back and soak in more water, lean to the left and do another ponytail squeeze.
I lean back and soak in more water and do a ponytail twist while leaning back. More water soaking and parting and then I lift my hair up to let the shower hit my nape for a good long soaking.
So I guess my answer is yes. I do rinse my hair very well before washing.
ETA: I did notice that I use a lot less shampoo once I started doing this.