No, the decorations were there from the earliest centuries of Christianity, long before there was any division between East and West. The buildings in Rome were built from the time Christianity became legal to now. Other places were sacred places to Christians even before Christianity became legal.
I assume you do know that if you go to the top of the dome of St. Peter's and drop a stone, that stone would fall on the burial place of Peter himself. The place was regarded as sacred by Christians in the earliest centuries but revealed only to those Romans who were known to be Christians, and when you visit the site, you will see the scratchings on the walls made by early pilgrims who visited the burial place of Peter.
If you go to Rome, make sure you write early to the place that handles tickets for the Scavi, that is, the excavations under St. Peter's. They take you through on a guided tour with a group of people from your language group. It's very hard to get in during the summer, but if you have time in the winter or early spring, it's not too difficult to get on a tour if you speak English. The guide who took us around was a Ukrainian seminarian whose English was charmingly correct!
Go to St Paul's Outside the Walls sometime if you want to see a glorious church - where the bodies of Sts. Cyril and Methodius, the Apostles to the Slavs, are buried. There was a Slavic Pilgrimage in the last century, and the church - even into the 21st century - is filled with things sent by the Eastern churches to honor Cyril and Methodius.
The wonderful thing about being Catholic or Orthodox is that you are in on it from the beginning, unlike people who have to declare that the "true church" went underground for nearly 1500 years and emerged in the person of a dyspeptic not-very-good monk in Germany.
Good going. Way to miss the whole point.