Yes, that appears to be the case.
I never tried adding other Sims to the household during this challenge before, but I have now. The original Sim, who started the challenge, still can't learn any skills but the two Sims I had her move in, just for testing purposes, are both learning skills. One, an adult, has learned Charisma and Parenting. The other, a Child, has learned Creativity.
No Skills, No Problem is probably my favorite challenge scenario. It's fun finding ways to earn money without using skills. My current Sim took a job as a Scientist. The Scientist career is based on breakthroughs, rather than skills, so it's one of the few careers where promotions are still possible. It also has a lot of cool gadgets with money-making potential.