I just got back from Rome, and can report on this.
As with many things in that wonderful city, it's not completely straightforward. At first I assumed the yellow box in the bus where you validate your paper ticket would be the same box to pay contactless, but that is not the case. In every bus I took, the contactless pay box that works with credit cards is on the opposite end of the bus from the yellow validation box.
From what I saw: red ATAC buses have the yellow validation box in the back, and the contactless pay box in the front. For the silver-gray buses, it is the opposite: ticket validation is in front, and contactless payment is in the back.
And although the entrance / exit doors are marked to restrict entrance and exit, from what I could tell, nobody paid attention, and just entered or exited wherever they wanted.
It's also a very good thing I figured this out, because on our last day, the ATAC police actually came though our bus and required proof of payment from all the riders. The inspection woman was very no-nonsense, and wouldn't accept the notification from the credit card company on my phone -- she actually took our credit card / phone, ran it through a machine she held, and verified that we had paid. I've heard travel horror stories about what happens if you can't prove payment, but we managed to get past that.