A number of issues, come to mind.
There would be quite a lot of voltage drop across the LED, probably around 1.5 to 2 volts, depending on LED colour. I.e. Lots of burden voltage.
There is usually a minimum current, below which an LED emits no light. This is probably many, many microamps or more.
If you need isolation, then why not measure the current (sensor, sense-resistor etc), then pass that signal through some kind of opto-isolator.
The signal could be transmitted digitally (very accurate, ADC or similar), using a linear opto-isolator (potentially much less accurate) or by turning the signal into something else, more easily measured on the other side, such as PWM duty cycle or VCO (voltage controlled oscillator).
There are many other ways of doing it (isolated), including transformers (especially AC current) and hall effect sensors.