This is my take on it is the answer is yes and no. It is not absolutely necessary to use the drones while playing. However, later in the course, Greg demonstrates doing just that. So since it is available, use it. You will hear the relations of the notes you are playing with core or tonic note and the intervals between while playing. I think this has helped me with ear training, as Greg indicates.
Here is what Greg writes concerning the drones:
“Use the Practice Drones to hum and sing along with to develop internal pitch recognition. Sing high and low on the pitch as well and for the best results, close your eyes while listening to yourself.
Play long tones at all volumes over the Practice Drones and be sure to stay in pitch.
Improvising over the drones is great fun; simply make it up. Hear the character of every note in the chromatic scale against the pitch of the Practice Drone.”
By the way, since you have gone through Greg’s first book, be sure to watch and read each lesson with new ears. In other words, don’t rush through. You may be way ahead of someone who is this is all game-changing, but his new descriptions may give you an ah-ha moment.
I might be wrong about this, but I do not think Greg discussed the “concert hall” breath and resonance in the first book. He may have mentioned resonances, but I understood this much better and it made a difference in my sound. Look at the “Many Lemons” video.
Bottom line: play the exercises with the drones.