As above, you can do it but I don't know as it would be economical. I can say for sure that the transport piece would have been a waste for us as we've walked almost everywhere in Rome over our couple of trips; have only jumped on the metro/urban trains a few times for specific reasons so we just purchased individual BIT tickets for those.
At most I wouldn't purchase more than one and plan carefully to try and get the good of it. Spend the rest of your time seeing all the free stuff (there's a lot of that, especially if you're into church art/architecture) and attractions the pass doesn't cover, like the Vatican.
And do be aware that if you use the pass for Galleria Borghese that you're still required to reserve a time slot in advance, and can only do that over the phone (instructions in the FAQ section of the pass website).