Drywall is installed in basements all the time. Ensuring the basement is dry and taking precautions to make sure it stays that way is key. The ceilings can also be drywalled as long as there are no mechanical access issues. It is no different than having wiring, plumbing, and HVAC on the first or second floors. The only components to take into consideration are clean-outs, shut-offs, or other important access points since they are typically located in the basement.