Is it appropriate for a priest to say Mass with his back to the congregation?
Yes, it is an acceptable option in the General Instruction of the Roman Missal (GIRM). However, I would take issue with the notion that in this option the priest is saying Mass "with his back to the people." Does a bus driver drive the bus "with his back to the people"? Does the pilot "turn his back on the people" to fly a plane?
In this option, the priest and the people are facing the same direction. It symbolizes the priest leading the people in the offering of the Eucharist, and through their prayers the people assist. This is called ad orientem; symbolically both the priest and the people are facing east (the direction from which Scripture says Jesus will return).
In the more common modern scenario, the priest is technically not facing the people. Both the priest and the people are facing Christ in the Eucharist.
The GIRM does not forbid ad orientem. It is silent on which direction the priest faces except for the times that he addresses the congregation. On those occasions the GIRM explicitly states the priest "faces the people and . . . ," which would make no sense if the priest was always facing the people. This instruction is useful only if the priest is not always facing the people.
Both Pope Benedict and Pope Francis have celebrated Mass ad orientem on certain occasions, and every priest has the right to celebrate the Mass in this way.