Yes, the Armenian Orthodox Chuch is Orthodox and has always been.
There are two Orthodox presences in Jerusalem (many more of course) because it is such an important place to so many local Orthodox Churches.
Everyone wants to be there.
If they are the same why do they fight? Why do Orthodox fight each other in so many places, taking each other to court, coming to blows even at funerals, throwing each other out of churches, even digging up the departed?