No, MAX31856 does not have sample and hold at the input as the ADC in MAX31856 is Sigma Delta ADC.
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, MAX31856 does not have sample and hold at the input as the ADC in MAX31856 is Sigma Delta ADC.