No, this would not be an option. When an OVUV Fault is present in the MAX31856 all conversions stop.
The presence of the OVUV fault will suspend conversions and the ability of the MAX31856 to detect other faults until the fault is no longer present.
MAX31856
Production
The MAX31856 performs cold-junction compensation and digitizes the signal from any type of thermocouple. The output data is formatted in degrees Celsius...
Datasheet
MAX31856 on Analog.com
No, this would not be an option. When an OVUV Fault is present in the MAX31856 all conversions stop.
The presence of the OVUV fault will suspend conversions and the ability of the MAX31856 to detect other faults until the fault is no longer present.