Its a matter of saturation and scraping. But gouging or pullin off the skin of the drywall will cause you to re think your plan.
On several jobs to do this very same thing, I have had to resort to re drywalling with 1/4 inch over this old drywall AFTER the cork was removed.
1/4 allows you to sneak up to existing trim and molding and caulk it in and not have to add new molding.
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