Yes, dry hopping will add bitterness, but not in the usual sense (which is iso-alpha acids). Dry hopping is done cold, so there is essentially no isomerization of alpha acids going on, which is what normally happens in the kettle boil. The bitterness that comes from dry hopping is mostly from polyphenols.

Can dry hopping cause bitterness?

Dry hopping can make beer less bitter or more bitter, depending on your starting IBUs (International Bitterness Units) and the amount of hops you use when dry hopping. This is due to the change in hop acid composition that takes place when you dry hop.

Does dry hopping contribute to Ibu?

Past research has shown that more extreme dry-hopping regimens can reduce IBUs in beer made with kettle hops bittering, New Belgium Brewing's Ross Koenigs suggests that dry hopping without kettle additions can add far more IBUs than previously thought.