Effects of increasing current on external noise and SNR for analog transmission
Does that affect the SNR or provide better noise immunity for EMI or
  capacitive coupling?


If you are going to consider the effects of driving an unbalanced signal (only one Rs) down a balanced line to a balanced receiver, the biggest problem is the unbalanced signal in the first place. It is unbalanced because there is only one Rs. To vastly improve the situation you apply another impedance of equal value in the 0 volt/return wire.

Now you have an impedance balanced transmission: -



Both wires are susceptible to EMI but, with a balanced impedance driver (due to having 2 x Rs), EMI affects both balanced wires the same and the receiver cancels those effects out.

There is no point considering the effects of EMI on a balanced cable unless you drive it with equal impedances (irrespective of whether you drive differential voltages or not).