Typically, yes.
Always. Unless you measure gravity twice, with a few days in between, and both readings are the same.
What's a week early? Is that what a recipe or kit instructions said? Nonsense. It's done fermenting when it's done fermenting.
Bulk conditioning is another matter. There are benefits to some beers to sit in the fermenter for a week or few after fermentation is complete. Clarity is one of the biggest. But if you skip that, fermentation having been measured and observed to be complete, the worst that will happen is more particulate in the bottle.