I have never met any mizrahi/sefaradi Jew who identifies as Arab Jew. There are but a few sick traitors who may identify as such. The thing is in the Arab world there was nothing close to progress and emancipation and civil society that has been in Europe. There was no national identity it was a society divided by religions, ethnicity, tribes and clans, till this day.
You might find very few and rare exception like some sick self hating communist Jews in Iraq who identified as Iraqis.