One thing though: without the shank and the pilot hole, do they allow the
things being fixed to pull together as the screw is tightened?

If you're screwing thin to thick, and the pull-up distance is small,
then yes. The force of an impact driver helps, as does the self-
countersinking action of the screw.

However if you're pulling something into shape, best to clearance
drill the attached part.