I am uneasy with your semantics. How does the arguement work when applied to other careers?
With a B. Sci I would not hesitate to call myself a Biologist, Physicist, Chemist, Geologist etc... Academic study is enough, even if I have never been employed in the field. Albeit, perhaps with the proviso 'amatuer'
With B. fine arts, I would call myself a sculptor, painter, visual artist etc... even if I've never been paid.
Similarly historian, philosopher etc... if you are educated, active and enquiring in the field, regardless of whether you are paid.
So what do you call someone learned in law, if not a lawyer? What if an individual was expert, fully qualified and licenced to practice law, and performed many of the functions of a lawyer for family and friends, such as providing legal advice, arguing in front of a judge, but was never formally employed or paid for this role?
I can not see why the above person is not a lawyer.