A friend had her chimney removed the way you describe a few years ago, followed by problems with damp in the bedroom next to the chimney.
She initially thought this was due to a leak on the roof or through the wall where the chimney was removed, when I went up the attic to have a look it turned out to be the warm humid air drafting up the open chimney and condensing in the cold attic. sealed the chimney at the fireplace end and the problems with damp went away.(Spell checked using UK English)
