Absolutely you can do this. In fact, this is where the term "dry hop" came from in the first place!
Back in the day, British breweries making bitters would take fresh hops in from the fields (which start out dry) and add them to their fermented beer in the cask to extract aroma. Then after the beer had been removed, they would take these used hops (which are now wet) and add them to the boil of a subsequent batch to extract bitterness. All hops were used twice in this way.
Hence the terminology: wet hops = bittering, dry hops = added to beer after fermentation.