Completely removing refrigerant from any vehicle when it is running is never a good idea because refrigerant is necessary to keep the oil flowing in the system. Additionally low pressure switches would cycle the compressor off which would defeat the purpose of doing it while running. Some AC service machines can fully charge a system with it not running as well.

Using a Robinair Model 17800B unit on 134a automotive Systems. Does not specify or address in manual.

If you are recovering the Freon then it does not need to be running, in fact it should not be running. If you are filling the system it does need to be running.

no. it does not need to run until you are testing it.