Low current more susceptible to noise?
The impedance that the input "sees" determines the amount of noise that will be present. The only possibly noise sources on that net are the output of OA1, the specified input noise of OA2 and anything getting onto the net via the transmission line.

Assuming that OA1's output is quiet and there is no external noise, the only noise is the internal noise generated by the op-amp's input but this only becomes a problem when the source impedance it sees is significantly high i.e. tens of kohms and above. This is not the case here because OA1 has a very low source impedance of a few ohms or tens of ohms at audio frequencies rising to hundreds of ohms as frequencies get higher.

This op-amp source impedance continues to rise but the transmission line saves the day because it will have capacitance to ground.

All of this has NOTHING to do with input bias currents.