Is my house MoCa ready? Cutting cord w/ OTA

I've looked and can't find an answer. Currently have Atlantic BB TV/Internet coming into the house thru one cable outside the garage. The cable goes into a splitter and 4 cables come out, which lead to 4 different rooms in my house. We have an Atlantic BB provided Gateway (modem/router) that is connected to one of those cords thru receptacle in dining room. I checked the model # of the gateway and it is MoCa ready. The other 3 cables lead to various rooms w/ Tivo DVR and Tivo minis. All that is going away. I'm having AtlanticBB turn off the TV, but we'll keep the internet. I've bought a new gateway that is MoCa ready that I intend to put where the old one was. I've got a new Roamio OTA that I intend to put in the bedroom w/ antenna connected. And a new Tivo mini to put in the living room. So here's the question, do I need anything else (like a Tivo Bridge)? Can I just plug all these Tivos into their respective walls and the MoCa-ready gateway will take care of it all? It can't be that easy, right?
Thanks for any help!