Well, I generally don't use the term "NCB" I say drug-free birth if that's what I mean, in large part because I think it more clearly communicates what I mean but also because "NCB" may imply that birthing in any way other than drug free is "unnatural" which to me has negative tone (sounds like I'm judging to me). I think that technically one could make the argument that a baby coming to live on the outside after cooking in-utero is the natural progression of things, even if the vagina is not the exit route or drugs were on-board (not suggesting that drugs are a great option or that they don't have negative effects on mom/baby, etc., just that they don't necessarily "contaminate" the birth, rendering it "unnatural").
When I refer to my births, I generally say that I had a drug-free midwife-assisted water birth for my first (and many folks would, and did, suggest that birthing a human in water is not natural). Of course I also hemorrhaged after she was born and again a couple days later and had TONS of drugs and blood transfusions and ultimately surgery as a result, so in my head the experience of the birth in totality did NOT feel very natural to me. When I speak of my second, I say that I had an emergency c-section (or surgical birth) as my DD was very intent on staying transverse breech. Her being transverse breech was just as "unnatural" as me trying to deliver her vaginally would have been. Likewise, the "unnatural" classical incision left on my uterus as a result combined with the "unnatural" pregnancy complications that have marked my current pregnancy will require another c-section. My birth will be a natural progression of my pregnancy to result in a safe delivery for me an baby even though it won't be a vaginal or drug-free delivery.
To be clear, I personally would always opt for a drug-free vaginal delivery if possible, because I think that it represents the best overall scenario for mother/baby, but I wouldn't want to suggest to any woman that the way they brought their child into the world was "unnatural."