According to discussions I had with the UNHCR last week, the documents that the residents in Nagorno-Karabakh possess would not automatically confer citizenship for Armenia. Therefore, they have emphasized that technically, they would be considered refugees, although many have close family ties.
They are encouraging the Government of Armenia to ensure that they are given a rapid process to become full citizens. This is largely a matter of technicality, given the close ties that exist between the communities, but the UNHCR has specified that some work will need to be done to naturalize them as Armenians.