Some fairly recent research has shown that dry hopping affects beer bitterness in a number of different, interesting and even unexpected ways.
To address the main question of whether or not dry hopping adds bitterness: it absolutely can (but not necessarily).
Hops, and especially hop pellets, contain humulinones, a recently-discovered oxidation ...
Its the overall oil content in hops that you're interested when dry hopping. Alpha-acids don't always reflect those amounts and the diversity. The data is available to some extent but you need to know the lot and manufacturer of the hops you have and track it back. Most homebrew shops don't track/offer that info with repackaged hops in-house.