You definitely want to allow some gap at the ceiling. I happened to allow just enough space for me to tilt the column upright from the ground and just clear the ceiling (1.5" gap). Ceilings are never perfectly flat/level either. It's just one less variable to fight with. The crown will cover the gap anyways.
It's challenging moving something that heavy into place with the gap let alone no gap since you can only lift it about an inch off the ground without scraping the ceiling.