When the outside fan on a central air unit come will compressor still kick on?

Yes, the compressor of a central air conditioning unit can still kick on even when the outside fan is not running. The outside fan is responsible for dissipating heat from the condenser coil, but the compressor is the main component that compresses the refrigerant and sends it through the refrigeration cycle. If the outside fan is not running, the condenser coil may overheat and cause the system to shut down, but the compressor can still start and run for a short period of time.