The Cougar head emblem does cover the old Mercury emblem's holes, but you do need to drill two new holes to fit the studs of the new emblem.
Note: Old (and new) emblem are held in place with a special double sided adhesive ring that you will cut through with fish line. Remove hatch liner to expose the old emblem's studs on the inside, gently push them out after you have cut the adhesive ring on the other side.