Can I smooth a knockdown-textured ceiling with spackle?
Spackle might work, however it is specially designed for repairing holes and cracks and is more expensive than the product that is normally used for doing a skim coat: regular joint compound or topping compound.
You should do a bit of research and plan to practice with wide trowels/mud knives if you intend to do this yourself. Hanging the drywall is not the skill-heavy part of the job; mudding and sanding IS. Professional plasterers spend years/decades acquiring the skills to skim coat, it is probably the most experience/skill dependent craft in the trade...