They are usually open until 18.30-19 hours. The priest does not sit in the church, he goes about his business. But they will always call the priest if necessary, and they will stay late if you need to pray. Downstairs there is a room with amazing acoustics, go, knock, you will not regret it. It's quiet inside, a church choir recording often sounds, very beautiful.
I was baptized here in October 2019, although I am Russian myself - but I love this cathedral very much, with all my heart. The service was in Armenian, and I was very moved by what was happening. Father Andronik is beautiful.