Checking the AC with the compressor running also allows technicians to identify potential problems or faults that may not be apparent when the compressor is off. Compressor issues, refrigerant leaks, or electrical problems can often be identified more effectively when the system is running.
On the other hand, if the purpose of the check is to perform specific repairs or maintenance tasks that require the AC to be turned off, then the compressor will be turned off during the check or repair.