I'm wanting to drill a piece of wood onto the ceiling as a cover for an old vent. Do I need to pre-drill a pilot hole first?
Typically, a pilot hole is used to create an "easier" path for driving a screw. In some cases, it is necessary to prevent wood from splitting due to the wedging forces applied by the screw.
Drilling a hole larger than the screw primary diameter will result in an easy driving but provides only for the head of the screw to retain the object being secured.
Having a hole slightly smaller than the primary diameter eases the driving forces, as noted above, and also allows for more "gripping" force of the item being secured, as the friction of the item against the shaft of the screw can be significant. This is mostly applicable if you wish a single point of attachment with minimal or zero rotation.
Screws are not usually loaded in shear, which means the head of the screw should be large enough to accept the forces applied to the item.
Allowing for your description, you would have to drill holes in both the board used as a cover and the portion into which the screws would be driven. In this situation, the holes in the board could be the same diameter as the major diameter of the screw, but the holes in the wood(?) surrounding the opening MUST be smaller diameter, no larger than the minor diameter of the screw (the portion between the threads).
Soft woods such as pine will tolerate smaller pilot holes, sometimes none at all, but that's risky. Hard woods and screws driven near edges of the wood will frequently split when fastened without pilot holes.
The above is a summary of similar information located here: Why Drill Pilot Holes