I am going to cage all my tomatoes this year. I had a terrible time last year with the ones that weren't staked/caged. It was mess. But then I am shooting for 160 plants this year:)

It depends on which type of Roma you're growing. Confusingly, Roma is both the name of a variety and the name of a group of similar varieties of paste tomatoes. Some are determinate, others are indeterminate. It is not strictly required to cage or stake any of them, but I feel like you have less disease issues and an easier time harvesting if you support even the determinate Roma varieties in some way. It doesn't have to be cages. It could be stakes (preferably more than one per plant, or it could be using the Florida Weave, for example.

If you're growing Roma VF, that one usually gets about 4' tall in my garden and I cage it, but it likely would do as well with just stakes. If you're growing one of the Roma types that is an indeterminate, a cage or Florida Weave would be better, but the world wouldn't end if you let the plants sprawl on the ground, assuming you have space to let them sprawl. It has been a long time since I've let any sprawl because, as Kim noted, they can turn into a big mess of tangled plants. Also, fruit on plants that sprawl on the ground tends to be slightly more prone to being eaten by varmints and to picking up diseases that involve fruit rot because they are closer to the ground.

About the only Roma variety I've grown that probably didn't absolutely need to be staked is Martino's Roma, which is a short determinate. It only gets 2 or 3' tall, but it is so heavily loaded with fruit that it tends to lean over and lean over and lean over from the weight of the fruit, so I still tend to stake it or cage it with a short cage when I grow it. That keeps it from leaning over so much that the heavy load of fruit touch the ground.

I would guess I lost half of my fruit from rot, bugs, and critters because of it being on the ground. Really sad. There were 30 plants in that section so you can imagine how many tomatoes were trash. I tried to stake cage and tie as I went along but it got ahead of me. This year I will have cage tunnels set asap

Yes, I have found that I must have the discipline to cage my tomatoes almost as soon as I plant them or I get busy and suddenly realize that they've gotten almost too big to cage. It can happen in the twinkle of an eye. I try to cage the same day I plant, but if I don't, then I try to come back and stake and cage the next day. There's nothing worse than trying to squeeze big, lush tomato plants into cages that they're already too big to fit inside of. It is just so easy to break off limbs and such while doing that.