Upvote:1
Doubtful. For several reasons.
First, you'd have to enter Turkey again (ie pass Immigration), pick up this extra piece of luggage, go to the check in counters, check it in, and go back to the transit area (security checks, immigration, go to gate, secondary security check). All that in two hours.
If you have one ticket, one one airline, Rome back to the US, via Istanbul (I suppose via Turkish airlines), your check-in is final in Rome, and you're not supposed to check in again along the way. Depending on the country, you might not even be allowed to leave the transit area.
I am not sure there is even a luggage storage facility in Istanbul, especially not after the terrorist attack there. You should check.
All in all, I doubt that this is possible. But you know what? Instead of asking here, you should talk to the airline. They have the knowledge and answer.