Are you sure it is "crown molding"?
Often people with lathe and plaster walls/ceilings mis-identify the molding aournd the perimeter of the ceiling as "crown molding". Instead, it may be what I know as "hanging molding". The molding actually sits about 1/4" below the ceiling level, and it is used to hang items on the wall using hooks and picture hanging wire. By this, you don't have to put a nail or some other hole in the plaster wall, which doesn't tolerate holes or banging with a hammer very well.
I have seen where people have used caulk to close that gap, not knowing/understanding the concept.
Without seeing your specific molding, I would think that if you had the traditional crown molding, it would have been difficult, if not impossible, to get the ceiling down without removing/damaging the molding.
Just my un-asked-for opinion
Jim
p.s. Isn't tearing lathe and plaster out a fun job??? Something to consider if you have more ceilings to do, you might be able to apply 1/2 drywall directly to the old plaster/lathe, or use furring strips to level it out if you have to; it is a LOT less messy, but still accomplishes a "new ceiling". I like to use screws; less banging means less breaking of the plaster keys.