I would suggest two separate circuits for these two devices. Moreover, I would further recommend that the generator fan be powered only when the generator is running (and not, for example, from shore power), which would suggest adding a panel between the generator and the transfer mechanism, with the radiator fan fed from this panel. Now the fan will run regardless of the position of the transfer mechanism, which is what you want.
All that said, the 1/2 HP motor on this pump probably draws around 6 amps. The maximum current a 20-amp circuit can carry indefinitely is 16 amps, so you should be OK so long as the motor starting current is less than 10 amps. That's a big if -- this pump is designed for water, so starting it with a more viscous fluid such as vegetable oil is a big unknown. The only way to know is to measure it under load with the oil at the lowest expected temperature (in the pump, not in the tank).