If it is not a good idea, is there any cheap easy way to "seal" the
ceiling so it's not dusty? It's old plaster with multiple repairs (old
and new) where pipes or electrical were run.

I seriously doubt that the old plaster on the ceiling is the source
of any significant amount of dust. If the basement is not currently
an occupied space, I'd just leave it as is, and take the ceiling
down and replace it as part of the renovations. What are the
walls?