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No importing of data is required. The actual share counts come from the social services (Facebook, Pinterest, etc). The plugin will periodically ask those services “how often has this URL been shared on your service?” and save that number in the database.
As long as the URLs are unchanged, the share count data should also be unchanged.
You could test this by installing Shared Counts but not enabling the buttons to appear on the frontend. When you edit a post, you’ll see the current share count for that post in the Shared Counts box in the right column of the editor.