The DC current will have to be switched off before a measurement is taken, otherwise the CT will saturate.

 

Consider also that the "leakage current range" is 80dB, and so the system will certainly require all of those three amplifiers, or perhaps four different ones to cover the 80 dB range span.
As for the concern about the DC bias voltage saturating the CT, consider that ten volts in series with one megohm will at most force one micro-amp to flow. Certainly that can be compensated for with the zero-offset adjustment. Yes, it does add some complexity, but as I have had to explain elsewhere, " It is difficult to tell the difference between zero and nothing."