Consider signalling/data/telecom circuits that are phantom powered - power flows down the cables that carry the signals (and up the shield if it has one). These configurations work reasonably well providing the currents that power the device are kept smooth and don't have a frequency content (with significant power levels) approaching the signal power levels at their lowest frequency.
If this is kept in mind, this type of system can work. Inductors are normally used to couple power to the signal lines and inductors are also used to remove power from the signal line. The data has to be (say) manchester encoded to make sure it's minimum frequency is well above harmonics of the power current of course. Other encoding methods such as scrambling or FSK are also commonly used in these circumstances. Differential/balanced encoding of the data is also important (see below).
So, to answer your question, NO the cable carrying current through its screen/shield is perfectly OK providing the harmonic content of those power currents don't interfere with the data either by induction or, to a lesser extent, by capacitive coupling - note that the data lines in the question are presumed balanced and differential so this meets some of the criteria mentioned above.
