Voltage measurement at different adc ground
No it will not work. The microcontroller ADC will measure the input voltage relative to its local ground. If this is not connected to the other ground, then this measurement will not accurately reflect the difference between the LDO output and Gnd 1. It's even possible that the to ADC signal is outside the power supply rails of the microcontroller, and could damage the micro.

If the ADC has a differential input option, and you can arrange that the 'To ADC' signal and 'Gnd 1' voltage will always be within the recommended input voltage range of the ADC, then you could measure this voltage using two connections and the differential mode of the ADC.

Otherwise, your options include


Use an external ADC grounded to 'Gnd 1' (and possibly some isolated data transfer mechanism like opto-couplers).
Use a "high-linearity optocoupler" (for example, HCNR-201) with an appropriate feedback circuit to transfer the analog voltage between the two ground domains.