Would any problems arise if I wired the current input to both the direct input terminal and external sensor input terminal?
You should not use the instrument with both the direct input and external sensor terminals wired. There would be a risk of electric shock or damage to the instrument since the external sensor input terminal’s Lo side, and the Lo side (+/- terminal side) of the current input terminal for direct input would both be at the same electric potential. When inputting a measurement signal to the direct input terminal, you must remove the shunt connected to the external sensor input terminal, and the current sensor.