Hi Alex,
From page 37 of the ADS1248 datasheet:
The means that any calibration command, register write or register read command requires that START be high when it is issued. So to answer your question, you do need to set the START pin high when you issue the calibration command. Once the command has been issued and decoded you can set the START pin low. The command will continue to function until completed even with the START pin set low.
Best regards,
Bob B