Common mode noise rejection and grounding instrument current transformer
If we just directly ground one transmission line and then measure voltage between ground and the ungrounded side, will there be negative implications for measurement of common mode noise on both transmission lines?

Yes there will. Consider this example circuit: -

The &quot;sensor&quot; might as well be a current transformer output and, if you have some length of balanced cable between it and your single-ended measurement circuit, then noise or interference won't be seen equally on both inputs of your single-ended amplifier. This is because the input impedances of the single-ended amplifier won't be equal. The &quot;balanced&quot; solution is to do this: -

Because both inputs into the differential receiving amplifier have the same impedance to local ground, the interference waveform is seen equally at both input nodes and, the effect of the differential amplifier is to cancel those signals out. This is a balanced input impedance.
Pictures from this longer answer.
Also, don't forget that your CT may require a burden resistor.