Churches come in all shapes and sizes. Some big, some small, some made of brick and some made of wood, some are beautiful and some are down right ugly. These are just buildings, they are places we worship in. See a church is not confined to 4 walls, a church is not confined to a building. The church of Jesus Christ, the Church of God’s is People, his people of every race and nation, who love Christ and are committed to serving him. Thats what a church is, its not a building,
I don’t know if you’ve had a chance to read through the thread, but it has been made clear that the original post was not about the appearances of the buildings (after all, in the Catholic Church, we have a wide variety of architectures, from the simple outdoor chapels of Africa with little more than a baldaccino over the priest’s head while he is saying Mass to keep off the sun and the rain, to the elaborate Gothic cathedrals of Europe, and everything in between.
Rather, he was talking about the liturgy (Order of Service) - if the Apostles were to attend your service, would they find a Rite of Penance at the beginning, followed by the readings from “the memoirs” as St. Justin called them in 140 AD, which we today refer to as the Scriptures, followed by the preparations for Holy Communion, with Holy Communion itself, and then the Rite of Dismissal (from which we get the word “Mass”) at the end.
its people, people like you and me, people of every walk of life who believe in the word of God and all that is stands for.So the answer to you question is yes. See the church is not what you call it, ie Protestant, Catholic, Baptist, non-denominatonal and so on. The church is people, not a title, but of people. You can call it what you want but we, all Christians, are the church. The church lives in all of us. So once again yes they would recognize them.
Not all of the people who call themselves Christians are heirs to the organization that the Apostles established (which is headed by Peter’s successor, the Bishop of Rome), nor to the Liturgy of the Mass that they established.
Being spiritually united with Christ is a good thing, of course - no one could be a Christian without that aspect of it, and if it’s all you have, it’s certainly a good starting place - but in 50 AD, or in 120 AD, it was assumed that, in addition to that, people were also members of the Catholic Church - and in fact, we know that, because the enemies of the Church focused on the membership classes, and tried to kill everyone in the membership classes, to prevent them from becoming Christians in the first place - but if a person could become a Christian simply by a private act of the will, without any external signs of having done so, then why would the Early Church have been bothering with membership classes?
The priest and his family are converting their home into the church. They’ll find a new home to live once the parish is more stable. 
But, you have to remember, they met in homes (and catacombs) because it was illegal to meet in public places for services. It would not make sense today to do that, unless out of necessity just to “imitate an Acts 2 church” as many are wont to do in America these days.