The alcohol content in beer is dependent on the amount of fermentable sugars in the recipe. Since hops don't have sugar - they don't add any alcohol to beer.
Since they are just the flower of a plant, hops do not break down into any fermentable sugars during the brewing process and they will not add any extra alcohol content to the final ABV of a beer.
Since dry-hopping uses the same hop flowers they will not add any fermentable sugar to the beer and, therefore, will not add any extra alcohol content to beer.
Hops have been added to beer to provide bitterness, flavor, and aroma since at least the year 822 AD. They also act as a natural preservative, help clarify the beer, and create/retain the head on the beer after pouring.