I checked out a few things and it might be possible! My guy was most of the way through "Family Matters" when the bed attacked. He hadn't finished the two aspirations or maxed the career yet.
Once he visited as a ghost, I had his widow marry him back into the household and had him look at jobs and kids on the computer. He can't Try for Baby, but he can adopt children and apply for jobs. The family aspirations are mostly social interactions with the kids, so those ought to be doable.
But I'll gladly abide by what the challenge team says - I just assumed (without asking) that if we invited a ghost back into the household they could keep working on the dreams, so if the rest of the team besides GlazeyLady doesn't agree, I'll drop him and assign the dream to another Sim.